I started at the bottom alphabetically, so here's what I've discovered. Of the list, the D/P egg moves are incompatible with Emerald Move Tutors unless they are also D/P TMs, where as the Advance egg moves are compatible with both D/P egg moves, D/P level-up moves and Emerald Move tutors. Also some combinations which I've checked to be illegal will be noted.
Smeargle is in the Ground egg group so the combinations of egg moves from that group will be easier to obtain. Also moves from XD are incompatible with any egg move (some XD Pokemon come with an egg move already learned in addition to their XD unique move, so they can have this move only). All other moves, including TMs and HMs and other level-up moves can be combined with these moves normally.
Note that some level up moves can only be gained in certain advance games (Destiny Bond can only be obtained for Qwilfish on Fire Red/Leaf Green for example) so those moves will likewise be incompatible with the D/P egg moves
Zangoose (ground egg group):
D/P unique egg moves: Fury Swipes, Night Slash, Double Hit, Metal Claw + all Advance egg moves
D/P unique level up moves: Embargo, X-Scissor, Close Combat
Level up moves: Scratch, Leer, Quick Attack, Fury Cutter, Slash, Pursuit, Crush Claw, Taunt, Detect, False Swipe
Advance egg moves: Flail, Double Kick, Razor Wind, Curse, Counter, Roar
Move Tutor moves: Dynamicpunch, Rollout, Snore, Icy Wind, Mud Slap, Ice Punch, Swagger, Swift, Defence Curl, Thunderpunch, Fire Punch, Mega Punch, Mega Kick, Body Slam, Double-Edge, Seismic Toss, Mimic (Counter) (Substitute, Swords Dance, Thunder Wave, Sleep Talk, Endure)
*Note: the first bracket here is for moves which are gained by egg move as well as Move Tutor. The second bracket are for those moves which are TMs in Diamond/Pearl
XD Move: Refresh (incompatible with egg moves)
Other unique event moves:
What this means, for example is that Zangoose cannot have Refresh combined with any egg move in it's moveset. It cannot also have any Move Tutor move except those that are now TMs in D/P (Substitute, Swords Dance, Thunder Wave, Sleep Talk and Endure, in this case) or also egg moves (Counter for example) combined with the new D/P egg moves listed above.
For practical purposes, this means the elemental punches are incompatible with Night Slash, as an example