22. caliber barrels are a pain to clean. First I run a patch with CLP or Rem Oil through. Then I use use a Boresnake. A few pulls and its good. Then I run a patch with CLP through the barrel again. I also stay away from lead bullets in all my 22 calibers. Messy.
The Reciever I just use patches and rags with CLP or Rem Oil to clean. Then a drop or 2 of Hoppes gun oil around the bolt. Badda-boom
On my AR's I only use CLP/Rem Oil. No gun oil.