Roy is punishable if you put things on shield, but if you space things out a bit, you can make life hard for them getting in. Weaving around their space and their options with our excellent mobility will help you find an opening to get in and punish. Dtilt and tip nair are the safest on shield, especially when you fast fall the nair. If you buffer rising fair in your short hop, you can execute a double jump or a special move before you land, which can help you get away from landing lag. If you attempt to land, though, you will incur the landing lag for fair. Roy can start things out of throws, and out of falling aerials (falling uair, nair 1, and people are working with sour bair as well now), and his moves flow together, but a lot of them are more trappy in nature, rather than guaranteed, which can make things rough. Roy has low air acceleration, which you can combat by angling your control stick in the direction you want to go while you execute your jump squat (for retreating aerials). Otherwise, once you're in the air, it's hard to retreat because of the low acceleration, though you can if you use your double jump (which gives you acceleration in the direction you hold when executed).
As for punishing oos, Roy's grounded up+b has super armor on startup, and can power through some faster options like jabs and whatnot and kill. However, be careful not to use this option too much, or you could be baited and punished hard for it. Also, make sure you execute it properly. It has super armor and KO power grounded, but if you are actually in the air when you execute, you lose both, so it becomes a bad option then. I'd recommend saving blazer for kills, which happen at fairly high percents tbh. Jab and ftilt can punish some laggier options, jab as a combo starter, and ftilt can kill when sweeted. Grab also works, though it's range is meh in general, as well as jumping OOS and coming down with nair (rising nair is a bit problematic, especially on shorter chars, but falling nair works).
Those are what I can think of off the top of my head, at least. Hope this helps!