My island's first villager birthday, Axel's, is tomorrow. I was planning on sending Axel a letter with a present but I don't know when villagers get the letters you send them.

Is it the next morning like you or does it happen right away?

Will they acknowledge if you sent them something on their birthday?

I also heard from someone that you can directly hand them a present at their party, which I don't remember happening before. Is this true?

I have him in my town as well, try stopping by his house today.

Yes they have a birthday party in their house on their birthday! One of my villagers had their birthday a few days ago. When you speak to them, you have the option to give them a present there