Which gun would be better for turkey a .22 -.22mag -.17hmr.
Also which one is best for hunting small birds or maybe crow.
Also what one would be cheaper for factory loads.
Could this calibers be used to effectivly shoot rabbits.

Any one of these would be okay for small game, crows, etc., but when you throw turkey
into the mix I'd opt for the 22 Mag. I have a Ruger 77/22 stainless steel with laminated stock target model in 22mag. It works great. I must admit however, I haven't thought
about using it on turkey, but have no doubt it would do the job handily if I chose to do so. Scoped it with a Leupold compact 3-9x. It likes Rem. V-Max, and also the CCI 40gr.
HPs (1/2" groups or better at 50yds.).

I agree. Anyone of those guns would be great for small game. But for a turkey or crow go for the .22 mag or .17hmr. I know for a fact that the .17 has no problems taking crows. The .17 and .22 mag rounds are about the same price dependig on which brand you choose. They cost about $10 for 50 rounds around here. The .22 LR bullets are definetly a lot cheaper.

i would go with the 22lr if you plane on shooting orplinking with it a lot and dont have a lot of money to spend on ammo i can get 550 rounds for 22lr for about $7 around here. i have 2 22's and love them because me and my son can shoot all day together for very little money. and have a blast doing it. they also work great on small game like rabbit's birds. there is even some very nice hunting hp ammo that is out now like the volositors,stingers ..... for a about $3-$4 for 50 rounds. i have never shot a 17cal so i can not tell you anything about them.