The switching circuitry for the 110V would need to be sized for whatever maximum load needs to be switched. If it's just 10W, then a small relay or a solid state switch could do the job. If the intent includes switching large and inductive loads like motors, then that needs to be known and designed for accordingly.
The way I read the description, the three stations are completely independent of each other. So while the three could be implemented with a single controller, each could be a standalone device with its own controller. The smallest microcontrollers (e.g. ATtiny85, less than $2 each) could be used in the latter case. I might favor three standalone devices, as it would reduce wiring and be simple to add additional stations if needed. But I don't understand the total scenario here, the purpose of the project.
I was a little vague.
Say I have a long table with three stations, each has a 10w power adapter coming from it. Red light on when power is off, green light on when power is on, yellow light on when 1/2 time remains.
The "button" is really a computer input. Could I send a "yes" to station 1 and have it turn on while 2 and 3 remain. Or even better, have the computer handle the timing.
The lights simply indicate the availability of current, "in-use." Is there a way to get a "server" to send the "on" signal to stations independently of each other.