Catch a Bidoof for Cut(Mute it when you use their HM moves), keep it until you get to the route after Hearthome(Which isn't that far in), catch a Bibarel, get rid of the Bidoof and teach it's moves to the Bibarel, and then keep that for eventually Surf and such.
What I want to know, is why you get the Strength HM over 4 gyms before you can use Strength. >_<
I think it had something to do with the way they shuffled around Gym orders, but I'm not sure. Out of all the Normal-type HM moves, though, it's the most useful in-battle, though.