1) To avoid confusing readers that don't know German or are used to umlauts: The correct transcription is base-vowel+e (i.e. ö turns to oe - the example given is therefor wrong. Probably just a typo, but still)
2) These transcriptions are lossy. If you see 'oe' in a word, you cannot (always) pronounce it as umlaut. The second e just might indicate that the o in oe is long.
3) ß is a character in the alphabet, as far as I'm aware and as far as the mighty Wikipedia is concerned, as I pointed out above. If you have better sources that claim something else, please share those (I .. am a native speaker, but no language expert. So I'm genuinely curious why you'd think that this letter isn't part of the alphabet).
Fun fact: I once had to revise all the documentation for a project, because the (huge, state-owned) Swiss customer refused perfectly valid German, stating "We don't have that letter here, we don't use it: Remove it".
Thanks a lot for making the effort and fact-checking better then I did there :).
For instance, in skiing competitions, the start lists are for some reason made with transcriptions to ASCII. It's quite okay that Schröder becomes Schroeder, but it is less desirable that Söderström becomes Soederstroem and quite infuriating that Hämäläinen becomes Haemaelaeinen. We'd like it to be Hamalainen, just drop the dots.
http://en.wikipedia.org/wiki/Diaeresis_%28diacritic%29
German has valid transcriptions to their base alphabet for those, e.g "Schreoder" is a valid way to write "Schröder".
ß, however, is a separate character that is not listed in the german alphabet, especially because some subgroups don't use it. (e.g. swiss german doesn't have it)