Here is the main list:
(A) Absorb, Acid, Acid Spray, Acrobatics, Aerial Ace, Air Cutter, Ancient Power, Aqua Jet, Arm Thrust, Assurance, Astonish, Avalanche,
(B) Barrage, Bind, Bite, Bone Rush, Bonemerang, Bubble, Bug Bite, Bulldoze, Bullet Punch, Bullet Seed,
(C) Charge Beam, Circle Throw, Clamp, Clear Smog, Comet Punch, Confusion, Constrict, Covet, Cut,
(D) Disarming Voice, Double Hit, Double Kick, Double Slap, Dragon Breath, Dragon Tail, Draining Kiss, Dual Chop,
(E) Echoed Voice, Electroweb, Ember,
(F) Fairy Wind, Fake Out, False Swipe, Feint, Feint Attack, Fell Stinger, Fire Spin, Flame Charge, Flame Wheel, Force Palm, Frost Breath, Fury Attack, Fury Cutter, Fury Swipes,
(G) Gear Grind, Gust,
(H) Heart Stamp, Hidden Power, Hold Back,
(I) Ice Ball, Ice Shard, Icicle Spear, Icy Wind, Incinerate, Infestation,
(J) None,
(K) Karate Chop,
(L) Leech Life, Lick,
(M) Mach Punch, Magical Leaf, Magnet Bomb, Mega Drain, Metal Claw, Mud Shot, Mud-Slap,
(N) Needle Arm, Nuzzle,
(O) Ominous Wind,
(P) Parabolic Charge, Pay Day, Payback, Peck, Pin Missile, Pluck, Poison Fang, Poison Sting, Poison Tail, Pound, Powder Snow, Power-Up Punch, Pursuit,
(Q) Quick Attack,
(R) Rage, Rapid Spin, Razor Leaf, Revenge, Rock Blast, Rock Smash, Rock Throw, Rock Tomb, Rolling Kick, Rollout, Round,
(S) Sand Tomb, Scratch, Shadow Punch, Shadow Sneak, Shock Wave, Silver Wind, Sky Drop, Smack Down, Smog, Snarl, Snore, Spike Cannon, Stored Power, Storm Throw, Struggle, Struggle Bug, Swift,
(T) Tackle, Tail Slap, Thief, Thunder Shock, Triple Kick, Twineedle, Twister,
(U) None,
(V) Vacuum Wave, Vice Grip, Vine Whip,
(W) Water Gun, Water Pulse, Water Shuriken, Weather Ball, Whirlpool, Wing Attack, and Wrap.
(X, Y, and Z) None.
These are the moves with multiple base powers that will activate technician if they meet their specific criteria:
- Beat up (if the user's attack does not exceed 550 from stat modifiers).
- Crush Grip (if the opponent's HP stat is at or below 49.1666...% [or 59/120]).
- Electro Ball (if the opponent's speed stat is higher than 50% of the user's).
- Flail (if the user's HP stat is 33% or higher).
- Fling (unless the move fails or the item you're holding is a Poison Barb).
- Frustration (if the user's friendship stat is 105 or higher).
- Grass Knot (if the opponent's weight stat is 110.0 lb [or 49.9 kg] or less).
- Gyro Ball (if the opponent's speed stat is 240% or slower than the user's).
- Heat Crash (if the opponent's weight stat is 50% or higher than the user's).
- Heavy Slam (if the opponent's weight stat is 50% or higher than the user's).
- Low Kick (if the opponent's weight stat is 110.0 lb [or 49.9 kg] or less).
- Magnitude (if the magnitude is 4, 5, or 6, which has a total 35% chance of happening per turn).
- Natural Gift (generation five only; if the user's item has a base power of 60 connected to it).
- Present (if the damage has a base of 40, which has a 40% chance of happening).
- Punishment (if the opponent has no current stat boosts).
- Return (if the user's friendship stat is 150 or lower).
- Reversal (if the user's HP stat is 36% or higher).
- Trump Card (if the move's PP stat is 2 or more).
- Wring Out (if the opponent's HP stat is at or below 49.1666...% [or 59/120]).
Source: PS! command /ms base power<60, base power>1, !status, all
and /ms base power=0, !status, all
and many Bulbapedia and Serebii articles for damage calculations.
Hope this helps.