Are you using lucky egg?

I stocked up >60 eggs at the beginning of L39, at the time when raid battes had not been inplemented. Now, I am at L40 and left with a dozen of eggs. These raid battles generate Xp faster than I thought.

No.

Maybe from 38 to 39 now since u can power up Pokemon to 40 without airplane mode or 3 device trick. At 39 or 40 I just don't see a point to use lucky eggs personally. I rather spend my coins on incubators, raid passes, super incubators and storage whenever they raise it to 1500 for Pokemon and 2000 for items. Stardust > useless xp.

I should, but I'm at lvl 31, almost 32, and gaining heaps of exp out of catching and raids anyway. Just waiting for a porygon or something to show up.

If you want to be able to take on a Level 4 raid with 1 other person instead of 4, then Lucky Eggs are useful. IF you have several hundred Stardust ready to use to pump up your preferred Pokémon to Level 39ish.

Other than that? You're Level 38, you're not likely to quit playing now. You'll get to Level 40 by the end of the release of Gen 3 most likely. There isn't that much of a reason to speed that up intentionally - if you get Lucky Eggs as part of a Special Box, where you're getting other things you're more interested in (say, Super-Incubators or Incense) it's not a waste, it's just a nice little bonus, not a necessity.