I actually tried adding alot in str when open beta started, since i didn't knew the influence of the stat. ( did it till around lvl 30) So i can, fron experience, say, that it is pretty worthless.
1 Str add 1 point to atack and 0,5 points to crit. you can forget the crit bonus right away, since you need 10 crit to have 1% crit rate! which means even if you would putt ALL your points into str, you would only get 2 % crit rate for it, which is less than one singel red crit rune provides.
The atack bonus is a little more visible, but its not overhelming either, on full str you would do maybe 10-15% more damage than a comparable full con or dex Warr, but it would leave you without any means to survive.
So as long as you dont have a really potent healer chained on you, you shouldn't add to much in str. and even if you have, you will still get some trouble on stronger bosses and in pvp, where you hp drop to fast to outheal.
As of what to chose between con and dex: I'm full con, so i can't tell on dex from my own experience. but from what i heared from other players a dex build is more of a solo build, while con is more for parties. Because even high hp will drop prety fast on harder mobs, but with some buffs from other classes and a heal now and then you should be pretty fine. While if you dodge most of the atacks, you can manage your hp more or less with only pots.
Btw i think splitting your points on a warrior isn't really helpfull (like going con/str or dex/str) since the bonuses the stats provide are pretty weak already, splitting them up would only lead to several weak effects instead of a stronger one.