The problem is that neither English and Norwegian are particularly logical when it comes to prepositions and often they follow different patterns. These are some of the major uses of 'på', 'om' and 'i'.
With regards to place, 'på' generally corresponds to 'on' or 'at', and 'i' to 'in' but there are lots of exceptions that just have to be learnt (e.g., 'på kjøkkenet' = 'in the kitchen').
'om' can mean 'about' ('Vi snakker om...' = 'We are talking about...'). It's also a conjunction meaning 'if'.
For time 'om' either means 'in'/'during' ('om sommeren' = 'in summer', 'om dagen' = 'during the day') or referring to a time from now ('om én time' = 'in one hour'/'one hour from now').
'i' means 'this' ('i år' = 'this year'; although some expressions with this sense don't actually use 'this' in English e.g. 'i dag' = 'today', 'i morgen' = 'tomorrow'). It also means 'for' ('i én time' = 'for one hour').
'på' means 'on' ('på mandag' = 'on Monday'). It also means 'before' or 'to' when telling the time ('fem på to' = 'five to two').
I think 'in the morning' can be translated as 'om morgenen' if you are talking about a routine event ('Jeg spiser frokost om morgenen' = 'I eat breakfast in the morning'). 'på morgenen' refers to a specific morning. It's the same sense as 'på mandag'. Compare the (archaic) English phrase 'on the morn'.
Nothing in the English sentence implies that the party is tomorrow, and I don't think the Norwegian sentence does either. It could be any date in the future. But off the top of my head I can't think of a context where it would make sense to say 'in the morning' when you were talking about today.