Pirates: Simple, easy, don't have any particularly strong ships. If you have a capitol ship, this crisis will be trivial.
Luddic Path: Effectively the same as pirates in terms of ship strength. They just throw more fleets at you.
Persean League: Utilize stealth and go dark. If your fleet can't take on the Grand Armada, then instead take out the two supply fleets.
Tri-Tachyon: Destroy a large number of their raid fleets, trade convoys, or disrupt their colony infrastructure via raids. Disrupting their colonies is the quickest and easiest way to defeating them if you don't mind hurting your reputation. Just remember to keep your transponder off and practice sneaking around to minimize your reputation hit.
Luddic Church: Lean a bit into anti-armor, you're gonna need it for those B R I C C s they throw at you.
Hegemony: There's no easy way to deal with this event. Just pack lots of anti-armor weapons on your ships and face them head on. They'll only send three AI investigations your way and once you survive them all, they give up.