RE: cleaning TC Omega
There are a couple pins that can be removed to remove the hammer/trigger assembly. When I had an Omega I usually just took a paper towell and placed it so crud from the breech couldn't get into the trigger when cleaning. About every couple of months (depending on how much shooting I was doing) I would spray the whole mechanism (with stock removed) with WD-40 and then blow it out with compressed air. Every 6 months to a year I would remove the pins and give it a good bath in boiling water.
Not sure what you call the pins, but they have a groove milled in them and a set-screw locks them in place. To remove, back the set-screw out a few turns and they should drop right out.