I need to know the literal meaning of this "I got to go to the party."
Did someone actually go to the party (as in I went to the party) or he had the opportunity of going to the party regardless of the fact whether he went to the party or not?
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The "literal" meaning of the rather "slangy" construction to get [to do something] is to have the opportunity [to do it] - always with the implication of taking up that opportunity (actually doing it).
In respect of future actions, if a 17-year-old Brit says I get to vote after my next birthday, that very strongly implies he intends to vote when he becomes eligible. If instead he'd said I will be able to vote... that strong implication of intending to vote wouldn't be there. So the be able to... version could reasonably be followed by ...but I doubt if I actually will vote, but that would be "unusual / acceptable" after the get to... version.
Note that [to] get [to] often just functions as an "auxiliary" verb in English, with little or no semantic content, so it's actually optional in the following example - which means the same regardless of whether get to is present or not...
1: I [get to] sleep easily when I avoid coffee
But with the "have the opportunity" idiomatic usage being asked about here, it makes a significant difference whether get to is present or not...
2: I [get to] sleep with my girlfriend when her parents are away
In #2 above, including get to forces the implication I am able to... [do something that I want to do]. If those two words aren't present, it's simply a neutral statement about what happens in that situation.
Finally, note that with OP's exact example, got is definitely a Past Tense usage (I was able to go to the party). But there's also the "Present" Tense / Infinitive usage to have [got] to do something, meaning to be obliged to do it. With that usage, auxiliary have is often omitted in casual speech, and go to is often transcribibed as a single word...
3: I gotta go to the party
(I must go to the party - but with the strong implication that I don't actually want to go)