Well hello there! When someone says "good day, fellow!" it's a polite way of saying hello and wishing you a good day.
Now, "axe handle" is a bit trickier. An axe is a tool with a sharp blade that people use for chopping wood or other things. A handle is the part you hold onto to swing the axe.
So when someone says "axe handle!" it could mean a few things. Maybe they're excited about chopping wood or using an axe. Or maybe they're just saying it as a funny, random phrase. Either way, it's not a very common expression so it might be a bit confusing!