Wrote the Yellow Wallpaper," she once visited a physician who advised her, upon learning of her issues with depression, to abandon all intellectual activity 

[...] a noted specialist in nervous diseases[...] put me to bed and applied the rest cure, [...] and sent me home with solemn advice to "live as domestic a life as far as possible," to "have but two hours' intellectual life a day," and "never to touch pen, brush, or pencil again" as long as I lived....

The result of this treatment was that Gilman completely broke down, reverting to one of the worst depressive episodes of her life. Hence, she wrote "The Yellow Wallpaper," in her own words, 

to save people from being driven crazy, and it worked

This being said, let's explore how many different examples of oppression, all of which Gilman experienced in her own skin, we can find in the story:

1.  "He does not believe that I am sick" 

Jane, the narrator, explains that her husband is a physician but that he does not believe in the reality of her feelings. 

If [...] one's own husband, assures friends and relatives that there is really nothing the matter with one but temporary nervous depression—a slight hysterical tendency—what is one to do?

The oppression here is caused by the utter disregard to the needs of this woman. She has been sending signals that she needs help, and she continues to be ignored, even by her own husband. The oppression comes in the form of pushing onto her the belief that "she is OK."

2. Jane's brother is also a physician who agrees with Jane's husband that there is nothing wrong with her. They both advise that she stops working—that her stimulation is taken away to rest. Still, she senses that there is something very wrong with that. 

Personally, I believe that congenial work, with excitement and change, would do me good. But what is one to do?

Again, she feels helpless: "What is one to do?" The oppression from the men in her life comes from demanding that she stops finding succor in work. They are also downplaying her emotions in the process. She is not free to be herself or to apply the treatment that she feels is needed. 

3. John, the husband, seems to want to take away everything that causes any inspiration in Jane. He closed the window of her room when he decided for Jane that something she felt was a draught. As a result, she became angry with him. Still, she doubts her right to be mad. 

I get unreasonably angry with John sometimes. I'm sure I never used to be so sensitive. I think it is due to this nervous condition. But John says if I feel so, I shall neglect proper self-control; so I take pains to control myself—before him, at least, and that makes me very tired.

She is trying too hard to comply with whatever her husband tells her to do. She does not realize that she is neglecting her own needs during a very delicate time and that her condition is truly serious. 

4. John, the husband, is so overbearing that she is starting to confuse his meddling with "caring." He is oppressing her to the point of causing her hide her writing from him. He is driving her crazy. 

There comes John, and I must put this away,—he hates to have me write a word.

5. John's disregard makes her feel unimportant. He refers to his other patients as "serious cases." That is a form of oppression because it shows that he is imposing upon her a false label of "wellness."

John does not know how much I really suffer. He knows there is no REASON to suffer, and that satisfies him.

6. Not only does John disregard his wife, but he also pushes her to snap out of her current state with the threat of sending her to a doctor that deals with cases of nervous breakdowns. She is scared, so she is forced to hide her condition even more.

John says if I don't pick up faster he shall send me to Weir Mitchell in the fall.

But I don't want to go there at all. I had a friend who was in his hands once, and she says he is just like John and my brother, only more so!

It is no wonder that she starts seeing a woman in the yellow wallpaper of the room, and it is no surprise that she breaks down completely trying to "liberate" the woman.

Outside of the feminist perspective provided above regarding the oppression in Gilman's "The Yellow Wallpaper", one could look at the oppression both the environment and mental defect have upon the unnamed protagonist of the story.

First, the room alone oppresses the protagonist. She finds it impossible to become well again (she is suffering from Post-partum depression) in a room as littered with evidence of past horrors. The scratched floor, marks in the bed posts, and (above all else) the wallpaper. The room alone oppresses the protagonist.

Outside of the environment, the post-partum depression oppresses the protagonist. Her inability to pull herself out of this mental deficiency adds to her oppression. No one really helps her overcome the PPD. Instead, she is left to fight against it on her own. The fact that the PPD oppresses her mentally speaks to the fact that she is driven even further into insanity.

First you might read Charlotte Perkins Gilman's "Why I Wrote the Yellow Wallpaper." See link. The story explores a very real oppression of women concerning childbearing and what many doctors of the time misunderstood about pregnancy and postpartum depression.  The "rest cure" was a treatment resulting from misunderstanding women, pregnancy, and how to best support new mothers.  Often those with authority such as doctors and men forced these treatments on women despite what women thought of the situation themselves.  For example, the protaganist wants to write. She knows that writing will make her feel better.  But she is forbidden to do anything that might overtax her.  You might also look at this as an opportunity to discuss the oppression of women writers at the time.

Definitely. You seem to have understood the main message of this story completely. What is so significant about the image of the woman who is trapped behind the yellow wallpaper, with the black lines acting as bars, is that it is a projected image of how the narrator herself feels and how she is treated by society and her husband. Note the way that she protests about the fact that she is forced to stay in this room and rest, even though she herself would like to go out and have some sort of mental stimulation. The figure of the woman and the yellow wallpaper itself therefore symbolises the way that she as a woman, and women in general in this patriarchal world, are restricted and trapped. Notice the following description:

And she is all the time trying to climb through. But nobody could climb through that pattern--it strangles so; I think that is why it has so many heads.

They get through, and then the pattern strangles them off and turns them upside down, and makes their eyes white!

The woman behind the wallpaper symbolises the narrator and her feelings of being trapped and unable to go out. The black lines of the pattern symbolise the way in which patriarchal society, in this case the narrator's husband, forces women to live restricted and unfulfilled lives and mercilessly subjugate women to accept this passive role that is akin to being a prisoner. What is far more disturbing is how the narrator, by the end of the story, assumes the role of this woman and is literally trapped behind the wallpaper herself.

Situational irony occurs when a situation or outcome is different from what a character (or characters) in a work of literature think it is or will be. Dramatic irony occurs when the audience knows what a character or characters do not know. (There is also verbal irony, in which words or utterances mean the opposite of their literal meaning.)

As you note, Gilman uses irony to comment on the oppressive nature of gender roles in Victorian society. In a nutshell, the main situational irony in the story is that the treatment the men think is the cure for the narrator's mental problems actually makes her far sicker. A second situational irony underlying this is the assumption that male wisdom and expertise is superior to female: that the men in question know better what the woman needs than she does.

Dramatic irony occurs as the audience becomes aware that the narrator is descending into psychosis while she does not.

Some ironic quotes would be as follows. The narrator says of her husband John, a physican, that he:

is practical in the extreme. He has no patience with faith, an intense horror of superstition, and he scoffs openly at any talk of things not to be felt and seen and put down in figures.

Of course, this "practical" nature is exactly the problem: this is precisely the irony of the situation. John's seemingly rational "strengths" are really limitations.

The irony of the situation is underscored again as the narrator suggests what really is the solution to her problems but which is rejected by the patriarchs with power:

Personally, I believe that congenial work, with excitement and change, would do me good.

She says "I get unreasonably angry with John sometimes." The irony is that her anger is not unreasonable, given that her real needs are entirely ignored. She says too:

John does not know how much I really suffer. He knows there is no reason to suffer, and that satisfies him.

Ironically, his short-sighted focus on reason is the core problem. Gilman makes that point again in a slightly different way when the narrator states the following:

It is so hard to talk with John about my case, because he is so wise, and because he loves me so.

The irony of John's wisdom and so-called love is that they are destroying the narrator.

As for dramatic irony, the narrator becomes increasingly fixated on the wallpaper as she decomposes:

I'm feeling ever so much better! I don't sleep much at night, for it is so interesting to watch developments, but I sleep a good deal in the daytime. In the daytime it is tiresome and perplexing. There are always new shoots on the fungus, and new shades of yellow all over it. I cannot keep count of them, though I have tried conscientiously.

The dramatic irony is that we as an audience know her statement of feeling better, her being up by night and sleeping by day, and her fixation on the wallpaper are all signs of her mental deterioration, not her improvement.

Both assumptions are present in Gilman's "The Yellow Wallpaper."  One of the most striking conditions featured is how the oppression of women can be seen as a historical fact.  Gilman's work operates as almost as a narrative on how the silencing of women's voices was an embedded part of American historical and social development.  This can be seen in several instances in the story.  It is not an accident that the woman narrator is unnamed.  She does not seem to have an identity and her voice that emerges to the reader is almost covertly communicated. This is reflected in how the narrator is constantly discouraged from writing or engaging in anything that is remotely assertive in terms of her identity.  She is unnamed and is not validated as a woman, reflective of the social attitudes of the time period.  At repeated moments, the narrator feels compelled to say that "he does not believe I am sick!"  This reflects a pattern of silencing the voice of women and ensuring that their narratives are not validated.  John's insistence that his wife "lacks self- control" is another example of how there is a dominant social stereotype that locks women in gender- stratified roles.  John's attitudes towards his wife is reflective of something more in the social setting and historical condition:

If a physician of high standing, and one's own husband, assures friends and relatives that there is really nothing the matter with one but temporary nervous depression--a slight hysterical tendency-- what is one to do? My brother is also a physician, and also of high standing, and he says the same thing.

John's paternalistic attitudes towards women is echoed on a larger level, as seen in how "friends and relatives" as well as the narrator's own brother do nothing to question John's diagnosis.  It is clear that the private narrative in which John fails to acknowledge his wife's voice is reflective of a wider condition.  This helps to emphasize the assumption that the short story displays the oppression of women as a historical fact.  

In explaining why she wrote the short story, Gilman underscores how literary texts mirror societal attitudes about gender.  Gilman suggests that she wrote the story to prevent women from suffering in silence:   

Being naturally moved to rejoicing by this narrow escape, I wrote The Yellow Wallpaper, with its embellishments and additions, to carry out the ideal (I never had hallucinations or objections to my mural decorations) and sent a copy to the physician who so nearly drove me mad. He never acknowledged it.

Two distinct realities emerge from this admission.  The first is that Gilman, herself, experienced the predicament of the narrator in the story.  Gilman's physician who prescribed the cure of "rest" silenced her voice to a point where she almost went insane.  This reflects how there was a distinct social attitude towards women, something that Gilman herself experienced.  At the same time, the fact that the physician "never acknowledged" her narrative helps to substantiate the need for literature to raise awareness about social attitudes regarding gender.  Gilman suggests that the end purpose of her writing the story was to "save people from being driven crazy, and it worked."  Gilman writes a literary text that mirrors social attitudes about gender in order to transform them.  It is in this reality in which the assumption about literary texts mirroring societal attitudes about gender becomes evident.