No not invulnurable, far from it...
Ever had a bad day?
How about Second Impact - The southern polarcap melts or evaporates, sea levels rise, half the planet's population gets wiped out, and halved once again by the subsequent wars...bad day indeed.
...and these things were cloned from the very thing responsible for that thing.
So I don't say invulnurable - even a nuke would be a major trouble for an Eva pilot, but when you have power akin to gods...one begins to wonder.
You better take some serious firepower - that positron thing sounds good - though in the series it took the entire power capacity of Japan just to get through an AT field.
Did I mention that Angels managed to screw an Eva-pilots mind?
Well those were Angels, yet Eva is well - almost an Angel...one begins to wonder.
BTW anyone interested watch Neon Genesis Evangelion *aka Shin Seiki Evangelion*
here's a linky for info:
http://www.lwhy.clara.net/nge/Evas are far from being all powerfull - especially since most run on a power cable, still - for 5 minutes, you better consider avoiding confrontation altogether - or meet a damon from hell...