What I call the Omnis are virtually interdependent. (Not sure of the spelling of the plural of Omni.)
Here is my list;
Omnicompetent: able to handle any situation.
Omnificent: unlimited or infinite in creative power.
Omnipotent: having unlimited or infinite authority, influence or power.
Omnipresent: present in all places at all times.
Omniscient: having unlimited or infinite awareness, understanding, and insight or all knowing.
Complete and total or absolute omnipotence can't be completely useful or fully excercised without omniscience. If you are not aware or knowledgeable about some aspect or characteristic of reality then you can't make yourself capable of understanding, interacting, or minipulating it. Absolute omnipotence would require omniscience to make full use of it.
This is virtually true of all the Omnis. The DS9 Prophets existing in the wormhole exist throughout time. They aren't trapped in our now. This is a limited form of omnipresence. An unrestricted form or absolute omnipresence would be what most consider God to be, immediately present in all places, dimensions, alternate universes, throughout all points in time thus omnipresent.
All the near godlike aliens in most SciFi franchises or stories are a limited form of the Omnis. Some seem to have more of one aspect of an Omni while having less of the others. Given the interdependence/interconnectedness of the Omnis I'm not sure they would exist. If they did I wouldn't think they would for long as I would expect the aqcuiral of one would put pressure on the entities to acquire the others.
Perhaps more accurately or precisely, a certain level of ability or level of awareness of the other Omnis is required to reach a particular level of any one Omni. Without them the level isn't achievable in any one Omni.
Also, as the higher levels are attained the more difficult the interaction with those of a lower level. At some point infinite patience would be required to communicate and educate an entity on a much lower awareness than you. They would appear extremely dim requiring what would seem to be inordinate amounts if time to educate or enlighten them.
The Q don't seem to exist at all points in time. They appear to be conscious of other points in time only when they focus their attention on it. This seems to be true when it comes to knowledge. They aren't fully aware of some knowledge until they focus on it. This is why those less knowledgeable will sometimes surprise them.
Of coarse we must entertain the possibility they ARE omniscient and possibly omnipresent but for our benifit act like they are not.