StratTele29 here.

I have been playing electric guitar (model: Squire Stratocaster) for 3 years now, and I still don't understand how, in classic punk-pop songs like Dirty Little Secret (The All American Rejects) Ticket Outta Loserville (Son of Dork) and 21st Century Breakdown (Green Day), there doesn't seem to be any particular strumming pattern all the way through, just a constant electric guitar. It sounds great. I was wondering how to do this, if it's either an amp setting, strumming in time with (and under) the drum beat, or something else entirely. How do I mimic this effect?

I believe they are just doing a constant down stroke. Watch a music video and you'll usually see them just striking down on the strings.