I was deported and am now living back in Los Angeles. Should I go back to my country? or stay here to fight for my residency?
Might as well go back. Illegal reentry after previous removal is a federal offense and subjects you to the "lifetime" bar to readmission, with no waiver available.
Kindly be advised that the answer above is only general in nature cannot be construed as legal advice, given that not enough facts are known. It is your responsibility to retain a lawyer to analyze the facts specific to your particular situation in order to give you specific advice. Specific answers will require cognizance of all pertinent facts about your case. Any answers offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship.
You may want to consult an attorney. You say you were deported, but is that really true? Were you given voluntary departure? You could have an attorney file a Freedom of Information Act request to look at your file just to make sure. If it is deportation, then i think you are out of luck.
How did you return to the US after your deportation? If you did so illegally, you may be subject to the "permanent bar". See an attorney.
Mr. Shusterman's (former INS Trial Attorney, 1976-82) response to your question is general in nature, as not all the facts are known to him. You should retain an attorney experienced in immigration law to review all the facts in your case in order to receive advice specific to your case. Mr. Shusterman's statement above does not create an attorney/client relationship.