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Hello. Thanks for the question.
If he's not bearing any weight on a leg, then I would be worried about a fracture. If he's able to bear weight, but he's sore and limping, I think more of a soft tissue injury. If it's both rear legs that are sore and weak, then I start to think about pelvic fractures. If you want to know for sure, you'll need x-rays.
If you want to try resting and some pain meds at home, you can go that route and give him a week or two. As for pain meds that are safe in cats, the only over the counter med safe is Aspirin. You can give 1/2 of an 81 mg baby aspirin every 1-2 days.
I hope this helps, let me know if you have any other questions.