Question

What are all the moves and abilities that raise or lower evasivness?

Answer 1

Moves:
1. Acupressure (Sharply Raises Random Stat - 1/6 for Evasion)
2. Defog (Lowers Opponents)
3. Double Team (Raises User's)
4. Foresight (Reset's Opponents)
5. Haze (Reset's All)
6. Minimize (Raises User's Sharply)
7. Miracle Eye (Reset's Opponents)
8. Odor Sleuth (Reset's Opponents)
9. Sweet Scent (Lowers Opponents)
Ignores:
10. Aerial Ace
11. Aura Sphere
12. Disarming Voice
13. Feint Attack
14. Magical Leaf
15. Magnet Bomb
16. Shadow Punch
17. Shock Wave
18. Swift
19. Telekinesis
20. Vital Throw

Abilities:
1. Sand Veil (Raise in Sand Storm)
2. Snow Cloak (Raise in Hailstorm)
3. Tangled Feet (Raise if Confused)

Source:
http://pokemondb.net/move/all
http://pokemondb.net/ability

Hope I helped! :)

Answer 2

Acupressure (Raises random stat)
Defog (Lowers)
Double Team (Raises)
Foresight (Resets opponent's Evasiveness)
Odor Sleuth (Resets opponent's Evasiveness)
Psych Up (Copies the opponent's stat changes)
Sweet Scent (Lowers)
Telekinesis (Ignores opponent's Evasiveness for three turns)
Topsy-Turvy (Reverses stat changes of opponent.)
Minimize (Raises)
Gravity (Lowers)
Source1
Source2