If you've fired it and haven't cleaned it yet, please do so as soon as possible. Black powder and Pyrodex residue are both hygroscopic, they will absorb moisture from the air. The fouling reacts with the moisture and becomes corrosive. Pyrodex is, of the two, the worst offender, but black powder is not far behind. A gun fired with either one should not be left uncleaned for very long.
Go to a sporting goods store, or the sporting goods section of your Wal-Mart or K-mart, and get yourself a wool mop, .44 or .45 caliber whichever they have. And if possible, a nylon cleaning brush. Metallic brushes shouldn't be used in a brass or bronze barrel, for obvious reasons. The mop alone is sufficient for BP cleanup, just work it a little more. My ¼-scale Napoleon has never seen a bristle, simply because no one sells a brush the right size.
The cleaning regimen for Pyrodex is the same as for black powder. Water with a good brand of dish detergent is the formula, and HOT is best. Your gun is small enough that getting enough hot water is not a problem. Scrub it good, then rinse clean. Then scrub it again.
Lather, rinse, repeat. Just like shampoo.
Nitro powder solvents won't work. There are some ready-mixed cleaners for black powder but they are mostly soapy water, with some nasty additives like ethylene glycol (antifreeze). I have a bottle of Black-Off that has been use once and will never be opened again. And because it's toxic waste, I can't just pour it out.
Get some pipe cleaners for the vent. Use Dills or whatever other brand you can find in the tobacco section of your supermarket or drugstore. DON'T use the decorative pipe cleaners from a craft store, some of these will disintegrate in hot water.
A little white vinegar soak beforehand will be good if it's sat for a day or two.
Oil is useless as a cleaning agent for BP and Pyrodex (don't know about the newer subs) because the fouling won't dissolve in oil. It will delay corrosion temporarily (it blocks out the moisture), if you have to put off cleanup, but then you have to get the oily mess out of the barrel. This is where a good grease-cutting dish detergent (Dawn or Ajax) comes in handy.
Properly cleaned and dried, your gun should require no oil, but it won't hurt it either.