I currently own a T3i almost exclusively for video, with the 18-55mm kit lens, the 50mm 1.8, and the 24mm 2.8
I would like to upgrade to a full frame camera, and I see that 5D Mkii can be bought for around 1,000 dollars, with body only. That seems like a good deal, but the lenses would probably be a killer. I would just like to upgrade from the T3i. I know the 50mm 1.8 works on the 5d, not sure bout the 18-55mm and I know the 24mm 2.8 does not work on it.
Whether a lens "works" on a camera typically means if the image the lens projects is large enough to cover the sensor. As long as the lenses you want to use project a large enough image you should be fine (you can look up Canon's website and it'll typically tell you if the lens is capable of filling APS-C, APC-H, or full-frame). If the lens cannot cover the sensor you'll get a black vignette around the edges of your image (because the image circle from the lens is not covering the sensor). You'll also need to make sure that your lens will mount and be controllable by your new body. Canon makes several different lens mounts for it's lens. The most common is EF. But there are EF-S and EF-M lenses as well. Just double check your lenses with whatever camera you want to move into.
For $1K you have a lot of options at your disposal. If you want a full frame Canon DSLR you can look at the Canon 6D. If you just want a Canon DSLR regardless of sensor size you can find some good deals on a 70D, 7D or 7D Mark II. Or just step up to a newer version within the line you're already familiar with - t5i or the upcoming t6i. If you want to switch brands you can look at the Panasonic GH4 or the Sony a7s (which you'll need adapters to mount your EF-mount Canon lenses to).
Keep in mind that NAB is next month and most every company will showcase their upcoming equipment there. So if you don't need another camera tomorrow, you may just wait and see if anything else gets released that hits your price points.