I've been in the US for 4 months on a J1 work and travel visa, and working for just under 2 months. My employer says they'll issue me a 1099 form, as no taxes have been withheld. I've earned around $2000.
(My sponsor is a separate company that runs J1 work and travel programs, and have recommended I find another job, as they can't vouch for this one. I've been continuing with this one while I search for another.)
Is this a violation of my visa? If so, is there anything I can get my employer to do that would help matters?

J-1 under Work & Travel program has a restriction that you must work for your sponsor only. You must discuss this issue with your sponsor whether it is OK to file tax based on 2 incomes. Who will issue 1099, etc.