I'll second Vesnoth, it's been a while since I last played it. Same with Heroes V, but I'm not really in the mood for those. In Heroes IV I'm a noob (though in V as well, but not as much), and for Heroes III, I agree, it's better on small templates (like m200) — long games have worn me out, which is why I don't play them anymore.
Warcraft? Well, I guess it's possible, I've already forgotten when I last played it. As for strategy games, Warhammer 40,000: Dawn of War also comes to mind. And if you want really quick matches, then (whispering) Hearthstone, but there are already tournaments for it on HeroesWorld.