This is indeed complicated to explain the difference between 그러니까 and 그래서. They basically involve same meaning. However 그러니까 is often used to warn something. For example 너는 숙제를 잘못했어, 그러니까 다시해야되 그건잘못된거야, 그러니까 다시는하지마 Well, there should be far more better examples, but as i am not professional it is also difficult for me to be very specific.. I hope this explanation helped you!

If you say "그러니까", that means the reason of a prior sentence. If I say "나는 잘생겼다. 그러니까 주위에 여자들이 많다.". It means "I'm handsome so that there are many girls around me.". It's not just for meanig "However" I guess. Anyway, "그런데" means little bit different. When we say "그런데", it has more negative meaning than "그러니까". If I say "나는 잘생겼다. 그런데 주위에 여자들이 많다.", that sentence is very awkard. However, we can say like this --> "나는 못생겼다. 그런데 주위에 여자들이 많다." It means "Although I'm ugly there are a lot of girls around me." See? I hope that if you use KaKao talk, just add me as your friend. My ID is "newyoker". I'll see you around in the mobie chat. Bye~!

그러니까: in general means SO 그래서: if it's an adverb then it means YES if it's used in the sentence as a conjonction then it means So or SO THAT if it's used as an adjectif then it means BE SUCH