I recently quit my job because I was expecting to get laid off or fired because our department was losing contracts, we were overmanned, and I was the newest employee. I had just finished training and was told I should find a permanent position in another department which is not what I was hired for. I am now told I have to pay back the relocation package, aside from realizing I should have let them fire me, I want to know if I truly have to pay it back or is there a way to avoid that?

I'd have to read your agreement but chances are you do owe them the money. You quit preemptively and may have not understood the company's long range plan. They were not obligated to hire you in the first place but they did. They are not obligated to offer relocation packages but they did. They gave you an option that you decided not to take. I think you need to pay them or ask for any position they can place you in. Any job is better than no job and it may release you from the repayment.

I don't need a job... I have one, getting a new job is not the issue, that is very easy.