Differences between ways to express obligation?


1) I know that, to express something that you must do, you can use 方{ほう}がいい
and, for a stronger feeling, べき.

2) I am also aware you can use conditionals like 〜なくちゃ、〜なきゃ、〜ないと to express
that you need to do something.

Though I understand the difference between 方がいい and べき, and I somewhat
understand the differences in 〜なくちゃ、〜なきゃ、and 〜ないと, I don't understand the
difference between those two groups. I don't understand the difference between
1 and 2.

Is there some sort of nuance I'm missing? Also, is there a difference between
something you **need** (by yourself) versus what you're **obligated to do**
(by society or rules or something)?

