Translation:I am not going to the party because I am dirty.
In English, "I am not going to the party" is generally used for talking about the future (i.e. "I am not going to the party tonight"). But as far as I understand it, iść refers to an action that is happening right now, i.e. "I am on my way / walking to the party right now." Am I understanding this correctly? Or can iść also have a quasi-future tense usage? I only ask, because while this English translation is correct word-by-word, the two sentences seem to have a pretty significant difference in my mind.
'Iść' in this context has similar meaning to 'to be going to'. Idę na imprezę we wtorek - I am going to the party on Tuesday. Today is Saturday and I am not a time traveler, but I am 99% certain that I will be there, I have a plan and I am going to do it.
Movement verbs - tricky in every language.
Yes, "na" here takes Accusative (it also takes Locative when it means that something is literally located on something).
People go with the 'negative sentence' interpretation too far. Apart from things that simply take Genitive, with some of them being indeed rather 'negative', Genitive occurs when a verb taking Accusative gets negated.
So... why not here? Because it's not the verb that takes Accusative, it's the preposition. And in such a situation, nothing changes.