그리고 is combination of 그렇다 and ~고.
~고 means `and`.
example : 먹고 티비를 보고 있어요 = I eat and watch the TV.
~서 means `and then`. It implies a chronological order or is used to introduce a causal clause.
example 1 : 먹어서 티비를 봤어요 = I ate and watched the TV after.
example 2 : 뭐라고? 늙어서 귀가 잘 안 들려, 크게 말해! = what ? I am old SO I don't hear well, speak louder ! (BECAUSE i am old I don't hear well).
Originally 서 has the meaning of `from` (ex. 여기에서 = from here, in here).
You can easily see why we use 서 to introduce a cause.
from A, B happened = A서 B (늙어서 귀가 안 들려 = from that I am old, I can't hear)
~와/과 means `together with`.
example : 오늘 저는 제 엄마와 공원에 다녀왔어요 = Today I went to the park with my mom.
~랑 is similar to ~와/과
example : 오늘 저는 제 엄마랑 공원에 다녀왔어요.
It would be too difficult to enumerate all the different cases, I just gave a very narrow explanation of each. I think you should note them on a paper and every time you encounter a sentence with one of them, write it down. The more you see different context the easier you would understand the usage of each. Because each can be used in many various situation.