Oil in the cylinder would make it easier to get the cases out, not harder (or, if there was enough oil, you'd get a kaboom). I've experienced this stickiness of cases myself, and there are/can be/ have been a variety of causes:
1- Shooting a longer-cased round in the same cylinder after a shorter-cased round that left fouling in the cylinder. Think shooting .357 mag after 38 Spec. The longer case sticks on the powder fouling that it has to ride over in order to chamber. This is not your problem, as your gun only shoots .38.
2- high pressure ammunition that is expanding the case so much it doesn't entirely snap back after firing. This is probably not your problem either.
3- Rough chambers (and I think this probably IS your problem). Cheaper, lower-end revolvers are often cheaper because certain steps in the manufacturing process are skipped to keep costs down. Revolver chambers require a very smooth surface to avoid the very problem you have. If there is any irregularity in the chamber, even a very minor one, the brass case will expand just enough to hang-up on the rough part after firing. these rough patches may not even be visible to the naked eye. The RIA 206 has a good reputation as a shooter, but it's cheap for a reason, and its just the sort of gun where a glitch like this could slide through.
Another possibility is that you never actually cleaned out the cylinder chambers individually. Low-pressure rounds (like Winchester WB) will allow powder gas, and hence fouling, to go down the case a ways. This will eventually foul the chambers for any length of cartridge, producing a situation similar to #1 above. You didn't say how you cleaned it, but make sure you clean every chamber with solvent and a brush.