How useful are rec letters from residency alumni?

I would say pretty influential

I mean when applying to a particular program, how effective are rec letters from graduates/alumni of that program.

That's what I thought you meant. If they were a well thought of resident at the program it would be a boost. I know it is at ours. Why would and alumni want a crappy resident at their old program.

Is it weird to ask the residency director of your home program to write you a LOR?

Some programs actually require it. I'm meeting with my home PD next week to have him write me a letter. It didn't seem weird to him that I was asking (esp since other students going into ortho at my school are doing the same thing)