as a language enthusiast, usually what i do is look on the wikipedia phonology page of the language i'm learning. for swedish it's http://en.wikipedia.org/wiki/Swedish_phonology , but before you do that, it's handy to learn the international phonetic alphabet, http://en.wikipedia.org/wiki/International_Phonetic_Alphabet#Letters not every sound of course, but only those occuring in your native language and in your target language.
Hmm... I'm sorry to say I don't know. I googled around a bit, but couldn't find any rules. It seems to depend a lot on the origin of the word: whether it is originally Nordic or has been borrowed from another language. But those influences are fro so long ago that you'd need to be an expert (I'm not) to know that a particular word isn't Nordic by origin.
This is also a common spelling error for native speakers who are bad spellers: they spell any "å" sound with an actual "å", although in effect it's most often written with an "o".
Unfortunately, there are no clear rules for this, it just has to be learnt (and the history of the word is no indication either). There are tendencies, but they are rarely absolute. The best rule of thumb that I can give you is that o is usually /u/ when long, and /o/ when short, but again, that's far from safe to bet on!
(btw 'otta' is pronounced with an /u/, maybe you meant 'åtta'?)
Look these examples:
1) Words that use "EN" article:
1.1) Woman is blue (kvinna är blå)
1.2) A woman is blue (En kvinna är blå)
1.3) Women are blue (Kvinnor är blåa)
1.4) The women are blue (Kvinnorna är blåa)
2) Words that use "ETT" article:
2.1) Äpple är blå (Apple is blue)
2.2) Ett äpple är blått (An apple is blue)
2.3) Äpplen är blåa (Apples are blue)
2.4) Äpplerna är blåa (The birds are blue)