Okay...so how do I find a home for it? What do I do?
If you're really lucky, a store might take it. Probably not, though, unless you can find a fairly compassionate owner who wants a new personal pet.
Classified ads are a good place. You could ask the local pet stores if you could put up a bulletin; I Know at petsmart you're allowed to do this for free at the front of the store, they have absolutely no problem re-homing a pet when the alternative is undesirable. There may even be some sort of animal rescue near you equipped for this. It's not super-likely, but it's worth a phone-call or two.
I know it's hard giving up a pet you've had for a long time. I had to do the same with a guinea pig I had. A small backstory; Guinea pigs don't live proper, happy, *clean* lives in those small cages they sell at the pet store. Even the "big" cages are too small. I found instructions on-line for building a much larger, more appropriate home; 5feet by 2.5feet, all for less than what you'd pay for even the smallest pet-store cage. When I moved into my apartment though, I just simply couldn't spare that much space. I wanted to keep him, he was great, I loved watching him run laps around his cage and hearing him squeek when I came home. But I knew I couldn't keep him if I couldn't home him properly. So I decided to give him, and his cage, away to a kid in my dad's 8th grade class. It hurt, but it felt good too.
Someone will care for your Oscar just as much as you do, you just have to help them find each-other.