Odd one out!

[Sonata]

Naganadel is the only one that is an evolved form

Igglybuff, Magby, and Happiny

 

[CF1994]

Happiny was not introduced in Generation II.

Kadabra, Gothorita, Duosion

 

[Sonata]

gothorita is the only Pokemon whose name isnt three syllables

Togepi, Togedemaru, Rowlet

 

[CF1994]

Togedemaru is not part of any evolution line, and is not part of the Flying Egg Group.

Celesteela, Skarmory, Magnezone

 

[Sonata]

Magnezone is the only one which evolves.

Gallade, Froslass, Bellossom

 

[CF1994]

Bellossom can be both male and female, whereas the other two can only be one or the other each.

Porygon, Budew, Togepi

 

[Sonata]

budew because it will only evolve once whereas the other two will evolve twice

Loudred, Chatot, Wigglytuff

 

[CF1994]

budew because it will only evolve once whereas the other two will evolve twice

Loudred, Chatot, Wigglytuff

The answer I was looking for was: Porygon can evolve twice at Level 1 due to it's evolutions being accessible via trading, while the other two can't evolve twice at Level 1. They need to level up with happiness to evolve twice.

As for your latest odd one out; Chatot is not part of any evolution line.

My odd one out:
Slowpoke, Mudkip, Froakie

 

[Sonata]

slowpoke is the only one with a split evolution

Golem, Dugtrio, Onix

 

[CF1994]

Onix can evolve through trading if holding a Metal Coat in the succeeding generation; Gen II.

Empoleon, Primarina, Feraligatr

 

[Sonata]

Feraligatr is the only one without a secondary typing

Breloom, Vileplume, Parasect

 

[VisionofMilotic]

Breelom. He's a Hoenn Pokemon, the other two are native to Kanto.

Iggybuff, Togepi, Cleffa?

 

[Sonata]

Togepi is the only one that's not a baby pokemon

Talonflame, Ho-Oh, Charizard

 

[Juno]

Ho-Oh is the only Legendary of the three

Bidoof, Patrat, Zigzagoon

 

[PageEmp]

The first one evolves at lvl 15, while the others evolve at lvl 20.

Crobat, Goodra, Scrafty

 

[strangerhypno]

Scrafty is a two stage

Kingdra/Ampharos/Flygon

 

[Juno]

Flygon and Kingdra innately have Dragon as their secondary type, while Ampharos only gains that in Mega form.

Abra, Spoink, Espurr

 

[VisionofMilotic]

Abra, the three stage evolution.

Smoochum, Wynaut, Mime Jr

 

[Damien.aspiring.fandev]

Post gen6, wynaut is the only of the three without a secondary typing,
idem for the evolved forms. Pre gen6, smoochum is the only dual-typed.

Lugia, Dialga, Groudon
Hint: involves altered variants

 

[CF1994]

Groudon has a cloned variant that only appears in the anime, whereas Lugia and Dialga's altered forms appear in the games.

Sliggoo, Dragonair, Shelgon