They give bonuses to units of a certain type in their stack, and are also stronger versions of the unit in question
Whether they are worth it is up to you to decide

Officers are very much so worth it. I would say the Officer you should almost always have on the field is the Infantry officer, it has the stats of a late game Mechanized Unit available from Day 1. It gives a boost to all other Infantry in a stack with it, including itself, also it boosts the speed of armored units traveling with it. The next best one has to be the Naval Officer, by itself it's the equivalent of a Destroyer, Cruiser and Frigate all in one unit. I would say the Tank Officer would be another good one since it stacks speed boost with the Infantry Officer to move even faster but also because you'll almost always be using some form of ground unit. I have not used the Fixed Wing, Rotary Wing or Submarine Officers that much so I can't really speak to their performance. I would say these Officers are nice to have if your army is mostly based or reliant on these units.

A fixed wing officer is my go to. You can move him in between your strikers or ASF(depending on what you need at the moment). A high ranking one does wonders. Bonuses matter and that's what officers do.

Some are, some are not.
Basiclly they are super expensive versons of units that are designed to exceed conventional stack limits.

They reduce the efficiency deficiency by adding stack bonuses in speed, def and offense.

The downside is, they require research slots, they are limited to a single unit and more importantly once they take damage or are killed, they get more expensive to replace upgrade and healing them can take weeks. You can infact deploy aircraft to groundbases and infantry to boats to reduce hitpoints and increase heal rate. But they become sitting ducks, if attacked and losing them is devastating.

Mostly i just stick to the Infantry commander and Naval commander.
Sub and SF commanders are okay aswell, depending on your stack type.
Tank commander is maybe the worse, as not many amphibious stackable types to support his stack.
Helicopter and Strike fighter can be decent but they are just super expensive aircraft which can't be healed easily so i tend to not invest in them, but a 8-12 stack of aircraft can still be highly efficent with a commander.

End of the day, you need the rank, to rank them up, but if you want to dominate the early game with your starting infantry, gather them up, add a commander and just send them on their way they do WORK!

excuse me but what the fuck

Normally, helicopters and aircraft are used in small 5 stacks, 100% efficiency.
Because of the bonuses from an aircraft commander, the movement bonus, the defensive bonus, the attack bonus, you can increase your stack sizes to 8-12 aircraft, and operate at lower efficiency levels, but still deal highly increased offensive damage.