"In that" means "because":
"For the reason that, because, as in In that you will be busy for the next few weeks, let's go over your paper now.*
"In that" can be used to introduce a dependent clause either before or after the main clause.
"In case that" and "in the event that" both mean "if something should happen."
"...... If it should happen that. For example, In case[that] he doesn't show up, we have a backup speaker. ."*
In this sentence, you could also use "in the event (that) he doesn't show up...." These phrases can be used in a dependent clause either before or after the main clause.
"In which case" means "under these circumstances" and has to go after an independent clause:
He might not show up, in which case we'll leave without him.
The Tigers are probably going to win the game tonight, in which case we won't have a victory party.
*The American Heritage Dictionary of Idioms by Christine Ammer. Houghton Mifflin Company. 1997