I checked the wiki to see if either of these have already been listed and/or killed, but turned up nothing. That said, apologies if I'm listing something that's already been done. Oh, and I'm not responsible for loss of sanity if you read these.

This first one is most certainly NSFW, possibly NSFB depending on your tolerance for badly-written sex and weird formatting. In essence, Asuka gets hormonal, has sex with Shinji and... well that's about it for 7 chapters (oh, there's some pseudo-Instrumentality stuff too)
http://www.fanfiction.net/s/5585802/1/Rough_Love

http://forum.evageeks.org/viewtopic.php?t=8093
This is just WTF in distilled form. There's a nice self-insert Stu, the grammar is terrible and the plot makes no sense (the devil appears to Shinji, EVAs vs 'demons', etc).
Oh, and there's a sequel which is much worse: http://forum.evageeks.org/viewtopic.php?t=8157