I have a custom 17 hmr built on a ruger 10/22 action. I was wondering what your methods of cleaning would be. Any help is great.

Just tear it down and clean everything. If you don't want to take the trigger group apart, shoot it full of carberator cleaner and blow it out with an air nozzle.
The barrel should be cleaned like any other rifle that shoots jacketed bullets.

Don't forget to get under the exractor(s) and lightly oil the recoil spring.

Depending on how involved you want to get, some 10/22 shooters have a hole drilled in the back of the action so they can remove the breechblock and clean from the rear.

I never have, but if I did I'd remove the breech block and put the cleaning rod through the barrel and mark where it touches and most likely drill it with a 3/16 drill bit. In a drill press or a mill.

I don't clean mine that much anyway, but made a bore guide out of a PVC end cap once in a fit of creativity.