When I shot an Omega (have since solditso I could buy more to try in my search forthe "perfect" inline) I always pulled the barreled action out of the stock for cleaning. I would usually (for just a "routine" cleaning between shooting sessions) take a cloth and lay over the breech block and action to keep dirt from falling in there. Pull the breech plug & clean the barrel & threads (& breech plug). Then remove the covering cloth (an old wash cloth works good) and clean the face of the breech block.
About every three months, or before a long storage session, I would pull the whole trigger assembly and carefully clean everything.
Never had any rust problems.
BTW - a good set of Q/D scope rings helps. I used T/C Maxima rings & bases so I could easily remove the scope. Very good rings & bases, it returned to zero every time!