Where do you get the hm strength Pokemon Mystery Dungeon explorers of the sky?

Answer 1

You can get the Strength HM from a blue-haired character in Nimbasa City in the building directly to the North of the Battle Institute. After entering into that building, he's in the very first room that you first enter in and you can find him near the top left area of the room.
Nimbasa City (Top Left Building)

Answer 2

You can find it at spinda's cafe if you use a silver prize ticket. I think there is another way to obtain it but I am not sure