What is the best HM Pack Mule in Generation V?
The only HM you need to complete the main storyline of Black and White is cut, and this is a one-time event (you need to Cut a tree down in the Dreamyard to progress the storyline). Because of this, other HM moves only allow access to hidden items or for convenience. The main HMs people use are Surf and Fly, and Ducklett / Swanna can both learn the two moves.
Ducklett can be found as a shadow on the Driftveil Drawbridge, and Swanna on the Marvelous Bridge. (I believe you cross the Driftveil Drawbridge before even obtaining Fly or Surf.)
If you want a Pokémon that can learn Cut and Strength, Patrat is available early in the game and can learn Cut. When it evolves into Watchog, you can teach it Strength. (No Pokémon in Gen V can learn all four moves you listed.)
Basculin fits 2/3 of your requirements. He has a decent attack (Base attack of 92, max attack of 311 at Level 100) and can be found relatively early (requires surf). He learns the following HMs:
- Cut
- Surf
- Waterfall
- Dive
So, he keeps his use as an HM machine after getting the rest of the HMs. Although, I believe Dive is only used in one spot.
I also have to mention the best fly user in the game: Golurk
Is there anything cooler than flying around on a golem at Mach speeds (according to Black's pokedex)?
He has a base attack of 124 (Max of 381 at Level 100). His unevolved form can be found in Dragonspiral Tower.
It learns the following HMs:
- Strength
- Fly (Only Golurk learns this one, Golett is unable to fly)
- Not an HM, but Flash can come in handy
If you have a suitable Water-type Pokémon, such as the one I use, Simipour, you can teach it Cut, Surf, Waterfall, and Dive. (Note that the elemental monkeys, including Panpour, from which Simipour evolves, can be caught at Pinwheel Forest with a 10% chance of encountering each one in rustling grass.) Other candidates include Basculin as mentioned by Rapida, and the fully-evolved starter Samurott as Grace Note mentioned.
For the other two HM moves, you can use Pidove or its evolved forms for Fly and Throh or Sawk for Strength. Personally, I use Kyurem for Fly and Lucario for Strength (both not available until after the first game clear).
Frillish can learn Surf, Dive, Waterfall and Flash. Not the moves you're looking for but still a good round up.