why was house finally able to walk? i remember that he ended up having to get his cane back but i was just curious as to what made it where he could walk for those few episodes?

In season 3 he got Ketamine when he was shot at the end of Season 2, which helped him walk without pain for the first 2 episodes.

In season 5 he tried methadone but stopped at the end of that episode.

xoxo

Meaning. It was so much fun watching him run and skateboard. In "No Reason", House got shot によって a husband of a patient that blamed House for his wife's death.
House hallucinated through most of that episode. He was walking through most of it and it was like he had already had the surgery. He basically hallucinated how they needed to treat him. In his hallucination Cuddy gave him ketamine while he was out because she had researched the study. "Ketamine" reboots the brain basically.
At the end of the episode, as they were rushing him to the ER to get him help for the gunshots he woke up long enough to tell them to tell Cuddy to give him "Ketamine".

So it took a while for the brain to begin telling him the leg hurt.