I'm not sure what, if any, impact his contract renegotiation will have on his cap number, but there are some WR-needy teams that can afford to claim him.
Barring a Matthew Stafford contact extension, I don't think the Rams can. I'm not even sure what Odell actually wants at this point. He could get claimed by the Texans and get 15 targets a week. His dad could make some sweet highlight vids for him there.
Teams like the Seahawks, Packers and Rams offer him a shot at contention, but there won't be a return to prime-career Odell with limited targets. The Raiders and Saints could give him targets and a shot at contending, but he'd still need to clear waivers.
The whole situation screams Raiders to me, but we'll see.