It is not the grammar that makes these sentences sound strange it is the actual meaning.
- I eat a pizza at 6 pm.
This means that you do so always, regularly, habitually. It sounds strange because to eat a pizza at 6pm as a regular habit sounds strange. If, instead, you said, 'I have my dinner at 6pm', that would not sound strange.
- I am eating a pizza at 6 pm.
This means that it is your intention to be in the act of eating a pizza at 6pm. Again it is not the grammar but the meaning of the words that makes this sound strange. Not using the contraction 'I'm' makes it sound even stranger as it makes it sound inappropriately formal for a statement about pizza. If you said, "I'm having a few beers at 6pm" this construction wouldn't sound strange.
Why would you be telling somebody of your intention to be engaged in the act of eating a pizza at a specific time?
There are some possibilities:
A: Will you join us for a hamburger? We're meeting at 7pm. B: I'd love to but I'm eating a pizza at 6 pm. I promised the kids.
A: How is the diet? B: I finished it yesterday. I can't wait to get off work. I'm eating a pizza at 6 pm with Mary then we're going to the movies at 8.00 and I'm having popcorn and sodas, then we're hitting a nightclub for cocktails.
