They are all roughly equivalent, especially in more informal language. 'Got' tends to be less formal and more casual. 'I got to' = 'I have to' = 'I need to' There can be vary degrees to how 'obligatory' the thing is in regular speech; it's not incredibly precise. 'I must' is the highest level obligation, but this is mostly found in written form.

It's expressing obligation. you got to [+ base verb] = you have got to [+ base verb] = you have to [+base verb} You can also hear other varieties in casual speech like "you gotta" or "ya gotta."