How feasible are power draining beams or similar weapons?
They're not, at least in terms of our present understanding of physics and the nature of power generation within our control.
As an example, from the movie Star Trek IV, Checkov and Uhura board the U.S.S. Enterprise (aircraft carrier) to collect the "high energy photons" that result from nuclear fission to help re-crystalize dilithium. An energy drain is detected by the crew of the Enterprise, and Checkov is caught. Ignoring the obvious problem of collecting photons through both a sealed reactor and a closed bulkhead, the drain would have never been detectable... because whatever "photons" were being collected were outside the power-generation process.
As used today, useful energy must be carried along a conductor. So long as it is on the conductor (including within any kind of equipment), it can only be tapped by physically touching the conductor. No intangible "channel" (which SciFi tends to call a "beam") can be opened that will conduct the energy elsewhere. This physical connection is what the answers posted before mine address.
But, what if the energy was broadcast?
Scientists and inventors have been monkeying around with Wireless power transfer almost since the beginning of the electrical age. They've come up with some elegant solutions. But, even here, you can't point an emission of any type that would suck the energy out of the air — at least that we know about or understand.
But, I can imagine the concept of an emitted stream of particles that would become excited when passing through broadcast power. Perhaps, theoretically, the charged particles could then create a conductive path back to the emitter, which had an embedded collector that drained the excess energy from the excited particles. That's not a lot different from a gaseous lightning rod. but now you're talking about using a consumable (the particles) that must be loaded onto and stored in your ship or defensive location. Once you've emitted all the particles, you lose the ability.
Note that I'm assuming you can't use an elementary stream of particles for this purpose, such as an electron, proton, or neutron stream. I'll leave it to WB members with a greater physics background than myself to suggest if using some sort of elementary particle is possible.
Couldn't I use that against power lines?
Well, yes, but remember that electricity (and probably all energy) tends to take the path of least resistance. That will certainly always be the conductive wire, not your particle beam. The idea only works for broadcast power because the stream's conductive path is better than plain air.
Well... I'm not interested in using broadcast power, what are my choices?
Your only choice, I believe, is to disrupt, not drain, the power. I can tell you from personal experience that when a lightning bolt strikes close to home, all kinds of electrical things are destroyed. The reason is simple: the electromagnetic field generated by the bolt couples energy onto house wiring, phone lines, and even the cables between computers and peripherals, in the same way generators produce electricity by passing wires through stationary magnetic fields. The power levels can (and did!) exceed the energy-carrying capacity of wires or the energy-absorbing capacity of circuitry, destroying them. (I had to pull burned phone cable from the walls and replace a printer using those old billion-wire parallel cables....)
This could be done with an electron stream. Ships would need to protect themselves, by coupling their hulls to some sort of grounding reference. But, where there's electricity, there's the ability to overpower.