Ignoring some of the total idiot responses.
Noise is the greatest enemy.
First 20M, that 33ft (give or take) so making that a square
along the ceiling means any room larger than 8.5ft square
has enough perimeter, feed it as dipole and trim for
resonance.. Obviously that is almost a closet. Average
is 12x14 room (52ft) that nearly large enough for a 40M
bent dipole. Let the ends go vertical to make 66ft. Also
possible is a 44ft doublet fed with parallel wire (Twinlead
or ladder line) and a tuner and likely good for 40 through
10M.
The real show stopper is noise but some bands may be
better than others. Strictly case by case as to what
bands are quieter. Try everything!
Power even at such close space under 20W is not
exceeding exposure limits for HF. The usual
problem with higher power is not user exposure
but getting into stereos and computer speakers
or fire alarms. QRP helps, good RX is critical.
Be very willing to experiment. Closed loops (fullwave)
are doable for 15, 12, and 10M with the average room
size and as we ascend the solar cycle they may be good
bands for smaller antennas. Generally they tend to be
less impacted by noise.
One last thing wire diameter for larger antennas is not
a limitation. So #28 magnet wire hidden outdoors with
similar fine wires as "twin wire" feed can work very well.
Suggestion is Polystealth #26 guage as its durable and
grayish black. The hard part with outdoors antennas
is installing without being seen installing it. As to cable
to the outside RG174 is small about 1/8 inch, getting that
around a window its frame or other ways is trivial. Twin
wire is easy, open window, close on it, exception is
metallic window frames.
As many suggest, keep it a low key thing, most people
have no understanding and will blame you for their fish
dying and everything else.
Allison