I just watched all 26 episodes in one sitting for the first time. Great show until episode 20 or so when it just gave me this gross feeling.

Watch the movies to complete the experience. Although if you didn't like the last episodes of the series then you probably won't like them much because they are very shocking.

That's exactly the scene I had in mind and it happens right at the beginning of the movie.
The fights are really intense and brutal also.

I was like 13 and approximately 4 inches away from the screen xD. Let's say I fell over in a dramatic fashion xD

I didn't enjoy the series very much. Sure, the general premise of the plot is quite nice and things do get interesting later on but I never really liked how the second part of the series was handled and also, for me at least, the ending was a total disaster (that's including the movies). It's one of those things that do build up an impressive premise and then fail to deliver when things should be clearing up (Guardian Devil - I am looking at you).
I know that my opinion is probably a rare one but I do not understand how can anybody like a protagonist like Shinji. He's downright the most annoying leading character I've seen in ananime for the last ten years or so, being overshadowed only by Kira from Gundam Seed.

I actually liked the End of Eva movie ending. Anyway, you can now watch the Rebuild movies, an alternate retelling.
One curiosity: in my country, this anime series were selected to an usual kid program time slot. I guess this is one of those perfect examples of people selecting shows basely only on the animation characteristics. They really *****d up many kids minds... Later it was changed to the 12pm-1am time slot :)

I personally enjoyed the episodes from 20 onwards the most, so I suppose its just a matter of taste, I have always enjoyed a good mindfuck. I personally enjoyed episode 25 and 26 better than the End of Evangelion retelling of them, but then that's probably because I prefered the more ambiguous ending it gave and that it made more sense once you knew the context it was in.
As for Shinji being an unlikable character, try putting any kid through that and see how well they turn out. I found him more interesting than yet another action-hero type.

I suppose I'd have some trouble simulating this given the fact that giant human DNA based robots are hard to come by :P.

You know, it's a Jap thing so it's OK :-P