Maybe, maybe not. It could be that fast-moving projectiles and high explosives are still the cheapest way for them to cause damage, in which case they’d be fighting with somewhat better versions of the same kind of weapon. If they’re not using the laws of physics we’re familiar with and have an economy we’re not familiar with it’s anyone’s guess.

If they don’t have extra laws of physics (and there’s great reason to think we know most of them) they’re going to arrive in a small-ish craft after traveling many years or even centuries, and we would have a pretty significant resource advantage. The main way I can think of they could win would be by unleashing some kind of small, self-replicating weapon we can’t effectively target. Anything else seems like it would be destroyed long before we’re worn down.

Also how do we not catch a disease from them or vice versa?

Probably easily. Diseases generally have to be adapted to their host, and alien biology is bound to be very different. Even on the off-chance there’s an exception, the aliens probably have some pretty advanced medicine as well. Invasive species ruining agriculture and our environment could be an issue, though!