'jestem po weselu'
Lit. I'm after a/the wedding.
Is this colloquial or standard Polish?
Rather colloquial.
Can this structure always replace a past tense?
No. In one way it can be a substitute for past tense. But be careful with it. It doesn't work if you want to express more complex sentences.
Just think of it as "I'm after X". Even if it doesn't make sense in English.
Also note that in a Polish translation the 2 following sentence are identical, and mean
exactly the same:
1. I've been to a wedding
2. I was on a wedding