Despite Espeon's offensive-leaning stats, it should use a support set because other Psychics do offensive roles better:
-Reflect
-Light Screen
-Psychic/Psyshock/Yawn
-Baton Pass
Nature: Timid
EVs: 252 HP/4 Def/252 Spe
Item: Light Clay
Ability: Magic Bounce
Hydration isn't worth using anymore because Drizzle got nerfed to only last 5 turns (8 with Damp Rock). While Water Absorb is redundant with Vaporeon's Water resistance, it's still the superior ability because it compensates for Vaporeon's lack of reliable recovery (while Wish does provide recovery on it, it can be unreliable at times):
-Wish
-Protect
-Scald
-Ice Beam/Roar/Toxic/Heal Bell
Nature: Bold
EVs: 248 HP/252 Def/8 SDef
Item: Leftovers
Ability: Water Absorb
Nothing much to say about Jolteon, really:
-Thunderbolt
-Volt Switch
-Signal Beam/Shadow Ball
-Hidden Power (Water/Ice/Grass)
Nature: Timid
EVs: 4 Def/252 SAtk/252 Spe
Item: Life Orb/Choice Specs
Ability: Volt Absorb
or
-Substitute
-Baton Pass
-Thunderbolt
-Wish/Hidden Power (Grass)
Nature: Timid
EVs: 80 HP/252 SAtk/176 Spe
Item: Leftovers
Ability: Volt Absorb
Inner Focus isn't worth it. Synchronize is the superior ability to discourage opponents from statusing Umbreon:
-Wish
-Protect
-Foul Play
-Heal Bell/Toxic
Nature: Calm
EVs: 252 HP/4 Def/252 SDef
Item: Leftovers
Ability: Synchronize
Sylveon's only ability should be Pixilate, as it makes Hyper Voice stronger than Moonblast. However, it doesn't affect moves that are already Fairy type. If this is a cartridge team, just stick to Moonblast + Cute Charm, but take note that it won't be as effective as the Hyper Voice + Pixilate version:
-Wish
-Protect
-Hyper Voice
-Heal Bell
Nature: Bold
EVs: 252 HP/216 Def/40 SDef
Item: Leftovers
Ability: Pixilate
or
-Hyper Voice
-Psyshock
-Shadow Ball
-Hidden Power (Fire/Ground)/Baton Pass
Nature: Modest
EVs: 244 HP/252 SAtk/12 Spe
Item: Choice Specs
Ability: Pixilate
Not much to say about Leafeon, either:
-Swords Dance
-Leaf Blade
-Knock Off/Double-Edge/Return
-Baton Pass/Synthesis/X-Scissor
Nature: Jolly/Adamant
EVs: 252 Atk/4 Def/252 Spe
Item: Life Orb/Meadow Plate/Miracle Seed