What does it means when Rich says, "This is the oppressor's language yet I needed it to talk to you"?
Rich is commenting about the difficulty in communicating her ideas adequately through language, specifically her own vernacular, or traditional language, as it were, because she would not be understood. And so it is with language: to make ourselves heard, we need to communicate in the listener's language, otherwise there would be no communication—the message would be lost.
In Rich's opinion, the language that has become the dominant tool of communication is that of the oppressor—the colonist, the slave master, the usurper, the one who has gained control through oppression, suppression and tyranny. Once the colonist, or oppressor, has forcibly asserted his authority, he would break down whatever was important in the culture he has subjected to his will. His language becomes the dominant force. The language of the oppressed eventually fades away and is finally lost. The language of the oppressor becomes the dominant tool for communication, so much so that if the oppressed uses his or her own vernacular, he or she is either misunderstood, derided, rejected outright, or even punished. Even the oppressed's own people would jeer and mock the individual for being "stupid," for example, for not mastering the oppressor's language.
This is true even today. The oppressed are therefore compelled to utilize the language of the oppressor to communicate effectively. He or she has no other option, for if he/she refuses to use the dominant language, he/she would not be able to communicate. His/her voice will go unheard, and if the oppressed should wish to protest and verbalize his/her dissatisfaction, it is the language of the oppressor that he/she has to use, else the protest will be meaningless.
What Rich is therefore saying is that she has no choice but to speak in the oppressor's language for it is the best tool of communication available in these circumstances. If she does not, she will not be understood.