The impulse engines of a starship are powered by fusion reactors. One overloaded impulse engine ejected from the ship is effectively a 99.75 megaton bomb, which suggests a total peak output for the impulse power systems somewhere around the petawatt range. Early Romulan ships only had impulse power systems, although they clearly have FTL capabilities. Ships using "impulse power" to fuel their warp drives are far slower than those that do not. UFP ships also have battery backups and a warp core, which is a peculiar type of matter-antimatter reactor. The engines of the U.S.S. Enterprise can produce a total real-space impulse in excess of 1022 kgm/s, transferring a similar order of magnitude of kinetic energy to a real-space object.
A phaser pistol's power pack holds several GJ of energy.
The U.S.S. Enterprise can casually deploy, from stores, a string of 210 "flashbulb" satellites with a total peak power ouput that fall somewhere in the range of a few exawatts each to levels absurd enough to not be relevant to discussion.
"The Doomsday Machine" gives us the yield for an impulse engine set to self-destruct. Presumably the engine does not include the full fuel reserves; further, the Enterprise has more than one impulse engine. The impulse power system does not in any event seem intended for long burns. Thus, total peak power output approaching a petawatt seems likely for the impulse plants, particularly considering that impulse power systems and the ship's batteries can be used to power weapons and shields.
Spock tries to use the Enterprise's deflectors to move an asteroid he describes as roughly the size of the moon, succeeding in shifting its path 0.013 degrees; he arrived too late for that angle to deflect the asteroid far enough from the planet to avert a collision. With the asteroid impacting in two months, that suggests the Enterprise was capable of shifting its velocity vector a couple meters per second - imparting somewhere within the orders of magnitude of 1022-1023 kgm/s and 1022-1023 joules of kinetic energy.
The personal phasers of the "Galileo Seven" had enough energy to put 150 extra pounds into orbit - this is the quantity that the shuttle was overweight by when launched with the aid of phasers. If each member of the away team had one, that means each phaser power pack had enough energy to lift 20 pounds into an unstable orbit - through the appropriate quantity of atmosphere in a shuttle with the drag coefficient of a brick - and then maintain thrust for a while. All things considered, this gives us several (1-5) gigajoules per fully charged hand phaser. This explains why overloading phasers are dangerous; an overloaded hand phaser with a full charge could potentially release as much energy as a ton of TNT. For comparison, a C cell - perhaps two of which could fit in the handle of a phaser pistol - stores about 50 kilojoules.
In"Operation: Annihilate!" Kirk deploys a network of 210 satellites to burn out the maddening neural parasites, at a height of 72 miles. The goal is to cook the parasites with a million candles per square inch of UV radiation. If the satellites in question could create a million candles per square inch intensity through 72 miles of vacuum in isolation and radiate omnidirectionally, then they would have an output of 15 exawatts each; if they only emitted in a downwards cone, this is still several exawatts per satellite. The power required to bathe the entire surface of the planet with a million candles per square inch would roughly 600,000 EW if the planet is earth sized - 2,900 EW per satellite. If we adjust this figure for atmospheric loss, the energy requirements become excessively high, even considering that this need not be sustained for a long time. The minimum figure (3150 EW total peak output) is to be preferred.