There's several variations on this (besides うぃーす, there's also うっす、おっす、ちーす and probably a few more that I'm not aware of), all of which are very informal masculine greetings. They don't really have a good English analogue - something like 'hey' or 'yo' or 'what's up' is probably the closest you'll get.
These are fairly masculine greetings, and the average girl probably won't come across much of a need for any of them - if I heard a girl use one, I'd assume she was just being silly. These are also very informal - you'd only ever use them with your equals or inferiors, and mostly only in informal situations (i.e. AFAIK two teachers might greet each other at a bar with one, but wouldn't greet each other at school with one). You could probably get away with calling them slang.
It's not correct to write it as うぃす, as that doesn't accurately reflect the pronunciation. As far as I know, no one shortens that vowel, so うぃす doesn't actually mean anything.
xfirst, soxibecomesぃ. To type the long vowel markerー, just type a dash-. – Jul 28 '14 at 18:10xwithltoo, if you like that better. – Sjiveru Jul 28 '14 at 18:46lworks on Windows, but not on OS X, whereliturns intoり. Happily,xworks everywhere, so I usually recommend that instead :-) – Jul 28 '14 at 19:50whiyields うぃ. Also worth pointing out:who,thi,dhi,thu,dhu,twu,dwu... – Zhen Lin Jul 28 '14 at 19:55wimay well be good enough depending on your IME - it works for me with fcitx/anthy. – Sjiveru Jul 28 '14 at 20:29wiworks on OS X, too! (You have to typewyito get ゐ.) – Jul 28 '14 at 20:32