Answer 1

There are just 3 moves that increase evasion. They are...

Acupressure: Acupressure raises a random stat - Attack, Defence,
Speed, Special Attack, Special Defence, Accuracy or Evasion - by two
stages. It will always choose a stat that is not already maximized.

Double Team: Double Team raises the user's Evasiveness by one stage,
thus making the user more difficult to hit.

Minimize: Minimize raises the user's Evasion by two stages, thus
making the user more difficult to hit. Stats can be raised to a
maximum of +6 stages each.

The moves Stomp and Steamroller hit with double power against a
Pokemon that has used Minimize.

source

Hope I helped out! PX ;}

Comments

Thanks PX! Upvote to all!

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I'm fine with this, but I did answer first, and you just expanded on my answer :P

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thanks here to help/ LL if it helps I'll upvote you when ya done.

Answer 2

Acupuncture(Only a 1in 6 chance though, also increases 2 stages)
Minimize(Raises evasion 2 stages)
Double Team(Raises 1 stage)

Source
Sorry but thats it right now!

Comments

Oh, and it's "Acupressure", not "Acupuncture" :P

Answer 3

Acupressure (random)
Double Team
Minimize

Note that Acupressure is not banned in competitive play, but Double Team and Minimize are.

Source