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The beams could be quite narrow. We did the calculations in a course I took and from what I recall, all of America's power could be compressed to a 15 meter beam. So they could probably just setup a no fly zone around the beam. Birds might still be a problem, but don't the alternatives (e.g. wind power) already kill birds?

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Lets say Im not very interested in practicality but just the theory of this. How does it work? How can I send power from one side of my room to the other if I don't care about paying more.

Unfortunately, it's been too long for me to speak with authority on the specifics of what energy levels would be safe to do that for. However, from what I recall, in general there shouldn't be anything preventing that at reasonably low power levels. You could also use something like: https://en.wikipedia.org/wiki/Waveguide_(radio_frequency)

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