NERD SONGS.

Why do you need nerd songs? What even is the definition of "nerd song"? Is that, like, whatever I'm listening to at any given moment?

Here are some general songs that I like due to being, well, kinda "nerdy", if you will.
Sid Icarus, by Machinae Supremacy (just a band I like)
New Math, by Tom Lehrer (the most "quintessential" NERDSONG i can think of off the top of my head)
Heavenly Star, by Genki Rockets (you can blame my girlfriend for this one, I have no idea where she got it from but the band is basically Child of Eden)
Beatdown (Strider Style), by Curt Blakeslee (from MS Paint Adventures which is basically this webcomic thingy, but really any of the Homestuck songs will qualify)
ANYTHING "Weird Al" Yankovic makes will qualify for this section

There are also video game songs. Since you said you have all the Pokemon songs, I'll spare you my Nimbasa City theme link that is my ringtone when my girlfriend calls me, and just add various other video game songs.
Speed Highway (Act 1), by the SEGA Sound Team (as seen on Sonic Generations not-3DS; not really a "song", there's no singing involved)
Radical Highway (Act 1), by the SEGA Sound Team (as seen on Sonic Generations 3DS; not really a "song", there's no singing involved)
Love Love Shine, by Ryu Kosaka (from Dance Dance Revolution)
smooooch・∀・, by kors k (from Beatmania IIDX)
Nanairo Nico Nico Douga [7 Colors], by various artists (you can blame my girlfriend for this one too)
Cara Mia, by A Capella Records (original by Ellen McLain) (one of the two ending songs for Portal 2; I prefer this version as a song though)
Ai no Uta, by Strawberry Flower (Pikmin song)
Super Mario World, by Hyadain (Hyadain is a guy that does every single voice in the songs he does)
Street Fighter II: The World Warrior, by Hyadain (Hyadain is THE ONLY PERSON SINGING IN THE SONG, and does every voice, even Chun-Li; made even more impressive by the fact that the singing is done based on the character theme, while still matching the main theme)

Then there are anime opening songs, which aren't ever "nerdy songs", so I don't think you'd want to listen to them, but I listen to them so I'll add them anyway.
Motteke! Sailor Fuku, by the Lucky Star girls whose voice actors I forget already (and yes I only watch it because I like to watch little girls dance)
Kage Sagashi, by Natsumi Kiyoura (the opening to Sketchbook ~full color'S~)
Higurashi no Naku Koro ni, by Eiko Shimamiya (the opening to the eponymous anime, although the video has spoilers so just try listen without watching lol)
Naraku no Hana, by Eiko Shimamiya (same dealie as the above with the spoiler warning, except for Higurashi Kai instead of normal Higurashi)
Dango Daikazoku, by Chata (the Clannad ending theme)
What's Up People, by Maximum the Hormone (one of the Death Note openings)

I think that's good enough, for starters. I'll make bigger lists later.