and we are also hearing Eveline's thoughts, rather than a detached narrator's.

The same stream-of-consciousness technique of hearing Eveline's thoughts occurs in the quote below:

Of course she had to work hard, both in the house and at business. What would they say of her in the Stores when they found out that she had run away with a fellow? Say she was a fool, perhaps; and her place would be filled up by advertisement. Miss Gavan would be glad. She had always had an edge on her.

We know these are Eveline's direct thoughts and not the narrator's because of the diction: the phrases "run away with a fellow" and Miss Gavan having "an edge on her" are the kind of slang Eveline would use.

Thus, we get a subjective story. We learn Eveline's take on things—both what she observes and what she thinks—but there is never a time that Joyce pulls back and provide a narrative voice that "normalizes" the story or tells us what to think. This makes this story a classic example of modernism, which tries to capture the fragmented subjectivity of human existence. We typically don't have anyone to interpret our—or other people's—lives for us.

The story features a limited third person narrative, which means that it is told from the perspective of a storyteller whose perceptions are limited to only what he or she knows about a character or characters. In this instance, the narrator tells us about what Eveline does, thinks and feels. This account, though, relates only to her. The narrator does not say much about the other characters, and does not divulge their thoughts or feelings. As far as these characters are concerned, the teller reports only what is observed.

For example, the narrator informs us that:

She sat at the window watching the evening invade the avenue. Her head was leaned against the window curtains and in her nostrils was the odour of dusty cretonne. She was tired.

We are also told that:

She looked round the room, reviewing all its familiar objects which she had dusted once a week for so many years, wondering where on earth all the dust came from. Perhaps she would never see again those familiar objects from which she had never dreamed of being divided. 

The two extracts illustrate the fact that the narrator not only reports on Eveline's actions but also knows her thoughts and feelings. The narrator also presents Eveline's observations and thus relates her perspective to the reader, as in the following extracts:

What would they say of her in the Stores when they found out that she had run away with a fellow? Say she was a fool, perhaps; and her place would be filled up by advertisement. Miss Gavan would be glad. She had always had an edge on her, especially whenever there were people listening.

How well she remembered the first time she had seen him; he was lodging in a house on the main road where she used to visit. It seemed a few weeks ago. He was standing at the gate, his peaked cap pushed back on his head and his hair tumbled forward over a face of bronze. 

Unlike an omniscient third person narrator, the storyteller does not share other characters' thoughts and feelings with the reader and merely reports on what is observed, as in the following example:

He rushed beyond the barrier and called to her to follow. He was shouted at to go on but he still called to her. 

"Eveline" is writien from a third person point of view.

"SHE sat at the window watching the evening invade the avenue. Her head was leaned against the window curtains and in her nostrils was the odour of dusty cretonne. She was tired." The story is told from the point of view of an unknown narrator.

The use of stream-of-consciousness by Joyce in "Eveline" serves a useful purpose. Getting inside Eveline's mind gives us an insight into her confused, disordered way of thinking. If Joyce had used another kind of narration, then we would have been presented with a much less ambiguous, much less interesting character. We might well have seen the choice facing Eveline as a relatively simple one—either to remain in Ireland, stuck in a suffocating, abusive home environment, or to take off to another country for a fresh start with her lover. But being privy to Eveline's innermost thoughts alerts us to the psychological complexity involved in the decision-making process. We may still find it hard to sympathize with Eveline's torpor and paralysis as her lover departs for a new life in Argentina, but thanks to the use of stream-of-consciousness, we can at least empathize with her.

"Eveline" takes place within the heroine's mind, so there is little action.  The narration is therefore stream-of-consciousness.  The reader sees Eveline's thoughts as they wander to different places and times.  The story is not presented in a linear fashion.  Instead, the reader gains information about the story and the heroine through her thoughts and memory.