He has a rough early game because he isn't that tanky and he doesn't do that much damage. But after a few waves you should have some 50-ish damage farmed on your Q. It doesn't sound like much, but add to that your damage and the bonus damage Q gives for a nasty punch. And combined with W and E there's really no way to escape losing a quarter of your hp, at which point you just start bullying the other guy.
This might not work for everyone, but this particular Jax wasn't all that tanky and he stupidly let me farm for the first ten minutes or so. By the time I got two kills on him I had sheen, and my single Q was chunking his HP like crazy, and funnily enough, his E doesn't work against Q
But yeah, with Nasus, all you really need is time. You tank up, and over time your damage grows to insane levels, this leads to silly teamfights where you just walk up to the enemy carry (who can't escape you because of W) and double tap their ass. You then switch targets and double tap their AP carry. By this time the teamfight is yours
Ninja edit:
Pantheon, hehehe, that guy
His entire thing is early game dominance. This means that you get your runes (if you have any) and masteries to give you as much flat damage as possible. You also start with Dorans blade, or if you're feeling confident with a regular Longsword and some potions (a single mana pot is helpful). You farm at level one. Once you hit level two you can chuck a few spears every now and then. Get E for easier farming. By level three you should constantly chuck spears at the enemy (be mindful of your mana, always have enough for a W-E combo). You should have your first kill around level for or five since the enemy will be low from constant spears and attacks that you'll be able to just W-E and autoattack for the kill (passive from is really awesome for this).
This of course depends heavily on your matchup, there's several exceptions but generally you'll learn most of them from facing champions. Be agressive and constantly harass however you can if you feel your enemy can't commit to a fight. If they do, stun them and walk away. As soon as you get level six, start ganking your mid, free kills are always good.