I'm learning about Nom, Dat and Akk now in class and no one can explain the difference between wen and wem in english so that I can understand when to ask either to determine whether it will be dat/akk...
Both mean who or whom...
English has lost the accusative dative distinction morphologically though it logically still exists: accusative is the case of the direct object and dative of the indirect object. Hence, both wen and wem are whom in English. There is a hint: whom in a dative sense can often be relaced by to whom while this is not possible in an accusative sense.
Example (dative): Whom did you give to book? To whom did you give the book?
Example (accusative): Whom did you see? *To whom did you see?
In colloquial speech, accusative whom is often replaced by who: Who did you see?
This is a temporal adjunct ("zeitliche Bestimmung"), not an object. Like all adverbials, temporal adjuncts have no case. You ask "wann" = English "when".
N.B.: It is true that "dieser Woche" is dative but this is required by the preposition in (if used in the sense of English in; in the sense of English into it requires the accusative); the entire phrase in dieser Woche is case-less.
Your question is not really about wen and wem, but more about when to use Akkusativ and Dativ in general.
Basically you have to study this when studying verbs. If you study "geben", at the same time you should memorize that geben uses Dativ for the person to whom something is given and Akkusativ for the thing which is given.