Haze Shenron is the first Shadow Dragon defeated and was born from the wish to bring back Bora. Since this was a small wish, this is likely the reason he is so weak.
Rage Shenron is the second Shadow Dragon defeated and was born from the wish to bring back Goku in order to fight Vegeta and Nappa. Though this also brought back one person, it was meant to save the people of Earth, which is likely the reason he was stronger than Haze.
Oceanus Shenron is the third Shadow Dragon defeated and was born from a wish that Oolong had made to screw up Emperor Pilaf's. He wished for a pair of panties and as such, she is extremely embarressed by the wish that created her. Oceanus is alternatively good and bad, since her wish was neutral.
Naturon Shenron is the fourth Shadow Dragon defeated and was created by the wish to restore all of Majin Vegeta's victims. Despite this being a rather large wish, Naturon is not very powerful on his own and relies on his ability to absorb creatures in order to fight.
Nuova Shenron is the fifth Shadow Dragon encountered, but not the fifth to be destroyed. He was born from the first truely selfish wish, King Piccolo's wish to return his youth, and as a result, he is very honorable and has strong morals. Nuova wasn't destroyed by Goku, but was instead destroyed by Syn Shenron, for his betrayal of the Shadow Dragons.
Eis Shenron is the sixth Shadow Dragon encountered and is the only Dragon to have two different wishes explained for his creation. In the anime, he states he was created by the wish to bring back all of King Piccolo's victims. But in Dragon Ball GT Perfect Files, it was stated that he was born from the wish to make everyone forget about Majin Buu. Either way, the good intentions of these wishes result in Eis being a very dirty fighter.
Syn Shenron, or Omega Shenron as he later came to be called, is the last of the Shadow Dragons. He was born from the wish to bring back everyone killed by Frieza and his men and as a result of so many people being brought back, is the most powerful dragon.
Red Ribbon Army