Okay, so the vekn rules cause both problems to have the exact same outcome.

So how do people deal 6 damage (5 normal, 1 aggr) vekn.net/forum/6-rules-questions/63147-r...ing-agg-damage#63147 in one strike of one round? As per person trying to explain in that topic.

New example: i fight a vamp with 3 blood.
So lets say I inflict 4 damage (2 normal, 2 aggravated) in a single strike of a single round. After the strike no cards are played, damage is resolved. The vamp is forced to take the normal damage first. He is now at one blood. The first point of aggravated lands him wounded and on his way to torpor. He burns the last point of aggravated with his final blood. The opposing vampire is now in torpor with zero blood.

New example. I fight a vamp with 3 blood.
I deal 4 normal damage. He burns 3 blood, cannot heal the 4th and becomes wounded and goes to torpor with zero blood.

New example. I fight a vamp with 2 blood. I deal 4 damage (2agrv). The vampire burns 2 blood for the first 2 regular damage. At zero blood it takes the first aggravated and goes to torpor. On its way to torpor it takes a last aggrv it cannot heal and that vamp burns on its way, stuff like fame doesnt activate.

New example. I fight a vamp with 2 blood. I deal in one strike of one round 4 damage. It takes two and gets down to zero blood. The third damage sends him on his way to torpor. The fourth has no effect.

Are these four examples correct?

All of your four examples are correct (and congratulations for such a good grasp of this relatively messy rule!).

Just a little nitpick: in your third example, the vampire never "goes to torpor" because, as you say, on his way there he takes the additional aggravated damage and burns (and this is why effects like Fame do not activate). The technical term (which is never used in games in real life) for this "on his way" status is that the Vampire is "wounded".