I'm pretty sure there is no situation when "w" takes Genitive. As for the others:

When "w" means simply "in", "inside", it take Locative. Which is pretty logical just looking at the name.

Accusative is used when "w":

• denotes some movement, direction
• denotes the time that something will take
• denotes some pattern or shape that something has

As the first of them is most important, compare: "Mam złamaną kość w nodze" (I have a broken bone in my leg) "Uderzyłem się w nogę" (I hit myself in the leg).

Also, days of the week + the word "weekend" are exceptions and take Accusative.

Preposition "we" is used instead of "w" in the following cases:

• When the next word begins with "w" or "f" followed by another consonant, thus forming a cluster of consonants that is very hard to pronounce : "we Francji", "we Wronkach", "we Fromborku", "we wnętrzach","we wrzosach", "we wrześniu", "we wtorek", "we wszystkim", "we wzorze", etc.
• Before pronoun "mnie": "we mnie"; before "mnie" and its other forms, all the propositions ending with consonant are used with added -e: "ze mnie", przede mnie", "nade mną".
• Habitually before some nouns: "we śnie" (but "w snach" - plural), "we Lwowie" (but "w Lwówku/we Lwówku" - a similar city name)

The above is the most important. Besides:

• Is optional before some other nouns, where cluster of consonants are a bit harder to pronounce: "we środę/w środę", "we czwartek/w czwartek", "we mgle/w mgle", "we mszy/w mszy", "we troje/w troje", "we trzech/w trzech", "we czwórkę/w czwórkę","we fioletach/w fioletach", "we młynie/w młynie"
• Before some other nouns only in set phrases, but not in other expressions: "dać się (komuś) we znaki" but "patrzeć w znaki".

Read also:

• Everything You Need to Know about Polish Prepositions
• w czy we?
• w – we, z – ze itp.
• w czy we? – po raz kolejny