What effect do Admirals/Generals/Commanders have?

Solution 1:

From a Gamefaqs walkthrough

Officers: Certain Characters can be different types of officers. You can find out which ones a character can be in their status menu. Basically, Officers enhance military units. Admirals enhance fleets, Generals enhance troops, and Commanders enhance fighters. Admirals and Commanders make their units faster and more responsive in Tactical Mode and Generals make their troops much stronger and more effective.

Basically, except for Generals, I don't notice Officers boosting your units combat effectiveness that much. Their main strength lies in their ability to drastically increase the detection ratings of their units. This can greatly increase your defenses against enemy covert missions. So, it would be a good idea to post an officer on your more important planets to protect them.

Even when you have an idle character and just don't have anything for him/her to do, you can always make them an officer for added defense in your territory, that way they're not being wasted.

Solution 2:

The Star Wars Wikia has an article that discusses Star Wars: Rebellion as well. On the subject of officers, it had this to say:

Some characters could be given military ranks by the player to put them in specific roles.

• An admiral increased a fleet's performance by enhancing firepower, shields and speed.

• A general increased the performance of troops and reduced the likelihood of successful enemy missions on a friendly planet.

• A commander increased the combat efficiency and speed of starfighter squadrons. Ship-based squadrons also launch faster with a commander present.

While it also does not describe the mathematics behind which stats matter, nor the amounts by which they are enhanced, it does list the specific things that are enhanced (firepower, shields, speed, etc...).