Let's have a look at each of them:
besides (preposition) means "in addition to".It precedes a noun/pronoun/gerund:
Besides working in a bookshop she looks after the garden.
besides (conjunction) means "in addition". It usually precedes its clause, but can follow it:
I can'tgo to the cinema; I'm busy . Besides, I don't have any money.
Note that moreover could replace besides here in more formal English.
Also, anyway or in any case could be used here in moreinformal English:
Anyway, I don't have any money .
otherwise can either be an adverb of manner or a conjuction.
otherwise as an adverb of manner usually comes after the verb:
I must be eatenslowly. Eaten otherwise (= in a different way) it is not as good as eaten slowly.
otherwise as a conjunction means "if not/or else":
He must be ill; otherwise he would go to the party.
or couldalso be used here in more colloquial English:
He must be ill or (else) we would go to the party.
So can either be an adverb of degree or a conjuction.
As an adverb of degree, so precedes itsadjective/adverb:
The dog was so cute that . . .
It was so cold outside that. . .
As a conjunction, so precedes its clause:
Our situation was difficult, so we asked for help.
However can bean adverb of degree and conjuction.
As an adverb of degree, however precedes its adjective/adverb and looks like this:
You couldn 't earn much, however hard you worked.
As a conjunction, howeverusually means "but". It can precede or follow its clause or come after the first word or phrase.
I'll offer it to Tom. However, he may not want it or He may not want it, however or Tom,...