Asura was a mini-star buster IIRC (destroyed a star which was smaller than our sun)
All Gods in DBZ have the following abilities.
Jurisdiction over their specified area (Clairvoyance: This also gives them the power to view all happening in the lower world) (e.g. Kami can sense and see all happenings on Earth from his Lookout)
Telepathy: Communication / Mind Reading
Teleportation: Kami, Kibito.
In DBZ their are several category of Gods
Planetary = Kami
Judge of the Dead = Enma Daio
King of the Worlds = Kaio
Leader of Kaio = Dai Kaio
Gods of the Kaio = Kaioshin
Leader of Kaioshin = Dai Kaioshin
There are also evil counterparts to the Kaio and Kaioshin, Makaio and Makaioshin.
Kaio and Kaioshin are both born from Fruits from the World Tree. Golden Fruits become Kaioshin.
Kaioshin and Kaio are not Immortal. Kaio's live for 75,000 years. Kaioshin live for more than 10,000,000 years.
God of Destruction Birusu from the movie "Battle of Gods" likely slots into the position near Kaioshin, since he relates to the balance of the Universe.
The current most powerful Gods in DBZ is Dai Kaioshin followed by South Kaioshin, they are stronger than SSJ3 Goku.
Birusu could prove to be more powerful or just as powerful as SSJ3 Goku, we will have to wait and see on that one.