I voted that the Barbarian still blocks the way. Since the spell is called "Invisibility" rather than "Intangibility", it only makes sense that the Orc cannot pass through him. (I have played video games where the one term is used to imply the other, but that particular form of invisibility was magical "one-way" intangibility where the affected character could attack enemies but could not be attacked back.)
Now, if the Orc had a Longsword or similar, he could of course hit the Dwarf with
that, since the Heroes can do the same thing with their own diagonal weaponry regardless of Invisibility.
torilen wrote:If the orc runs into the barbarian, attempting to leave the room, the barbarian is going to
have to defend himself (technically). The way I see it, this would negate the whole "cannot
attack" part of the spell, and he would become visible again.
I'm operating on the assumption that the spell's "no-attacks" clause is purely for gameplay purposes, though, since in practice invisible characters often do make attacks while invisible. In flavor terms, defending oneself is different from actively attacking the monsters (a weak excuse, but it's the best I could get atm). It's a poor sort of invisibility where the enemy can break it by accidentally finding you in the midst of a melee.
Adding on to Big Bene's thoughts, yes, the Orc could try to push through the invisible Barbarian, but it would be exceptionally dumb to knowingly walk into sword range of an enemy you cannot see. Maybe he would do it if he was afflicted by a fog of rage or something, but at that point we're no longer talking Invisibility interactions so much as role-play house-rules.