In the first town area, Shrouded Hills when I go to fight those bandits I end up getting knocked over by one of the half ogres and I can't get up. So they have plenty of time to kick the crap out of me until I die.
Is there some way to get up faster after being knocked over, or at least some way to not get knocked over?
This is on turn based as well.

Can't help you with the knockdown but . . . I threw down some railroad spikes and they equipped them which made them a little easier, used the grenade on the leader and the stun grenades on the orcs, took me a couple of tries to get the throwing right . . .=)
Edit: Didn't really throw them, placed them from the quick bar.

I had the same problem.
I managed to kill Lukan and one Half Ogre and then the remaining one always knocked me and Virgil out and trampled us to death.
What I did was grab Dynamite from the local store, waited until it was dark, then i prowled into throwing distance of lukan and the front half ogre and threw the dynamite in between them. Both died a horrible death.
Because I was prowling they didn't notice the dynamite, so they stood there without going aggressive and waited until they were blown apart.
When i returned to loot the spoils of my reign, the remaining half ogre was still standing there, as if nothing had happened. He would let me pass without even thinking of attacking me. I killed him anyway.

When you were "knocked down" was your fatigue score at or below 0?
In Arcanum, having a Fatigue of less than 0 means that you're too weak to stand up and won't be able to fight again until your fatigue is raised. Many melee weapons (and fists) do fatigue damage, and so the ogres you speak of are literally beating you unconscious before finally killing you. The only way to prevent this is to prevent them from hitting you, or to kill them before they knock you down.

I didn't look at my fatigue when I fell over, but that was probably the case.

Death by Fatigue Failure is the leading cause of death for spellcasters (who use fatigue to cast spells) and people who consistently outspend their action points (which also drains fatigue). After your HP, your fatigue is probably your most important stat.

In turn based mode actions cost points (action points), there is a little bar on the left side of the action points meter and the lights will also change colour to display when you are trying to perform an action exceeding your available action points (it draws the excess from your fatigue).
You can quite literally be helping an enemy knock you out by trying to do too much each turn.

If you are in real time mode you can open your inventory and use a stamina potion while you are knocked down to stand back up.

keep your blue icon filled up just advance the time by a hour or 2
also when you are hit it drains fat.