Firstly, there are other pages here that have some answers...
http://www.atariage.com/forums/index.php?showtopic=8475
http://www.atariage.com/forums/index.php?showtopic=7745
The first has some names of the artists in question. As for media, I'll hazard a few guesses that might get you going in the right direction if you're creating art in these styles.
3D Tic Tac Toe, Berzerk, Space Invaders, Galaxian, Video Pinball and Yars' Revenge seem to be airbrushed.
Football, Home Run, Indy 500, Human Cannonball, Air-Sea Battle, Bowling, and Breakout seem to be by the same artist (judging by the signature) and look to be executed in watercolor with either a pencil rough underneath or pen & ink linework either underneath or on top.
Haunted House, Video Checkers, Night Driver and Warlords seem to be done by the same artist, in what looks like watercolor and colored pencils.
Blackjack looks like colored pencils.
Missile Command and Asteroids look like guache to me.
Adventure looks like watercolor.
I think Ms. Pac-Man, Centipede, Raiders of the Lost Ark and E.T. are also airbrushed.
Pac-Man looks like guache or acrylics with airbrush.
Hope this was helpful.