I do not have printed (paper) dictionaries, so I use the on-line versions of the dictionaries.
sb in the Cambridge Dictionary:
sb = written abbreviation for somebody or someone
sth in the Cambridge Dictionary
sth = written abbreviation for something
Of course, several words / expressions can be abbreviated as sb or sth.
Sb = stibium (antimonium)
SB = Sound Blaster
other uses for sb
other uses of sth
I found all that with a simple Google search. All information was on the first page of results. I will not copy / paste all definitions from all dictionaries, as it is not the point.
Are these proper words?
Hell, no! :) They are abbreviations, of course (I hope).
I already asked a specific question here.
Can I use these words in my essays, for example?
As far as I know, academic papers, like any formal communication, should use the minimum amount of abbreviation. Of course, some "famous" abbreviations are allowed (etc., e.g., i.e., names of institutions...), but other than that, not really.
Can I use these words in my posts on Stack Exchange?
Stack Exchange is a (mostly) informal place of communication, so abbreviations are not forbidden. However, their use can be ambiguous, and they should either be avoided, or disambiguated (defined).
Example: one question was about PC. The first words that popped into my head when I saw that, were "Personal Computer". However, OP meant "Politically Correct".