I installed a honeywell he240 humidifier 2 days ago and the solenoid randomly makes clicking sounds for 2-3 minutes then stops. I checked the water source and the valve is open. The water lines are clear with no air bubbles and there isn't sediment in valve entry. Any idea what could be causing this?

solonoid valve not shutting off on water line .

Sounds like the high pitched noise is coming from the solenoid valve which allows water to enter the humidifier. Typically when the water pressure is too high, it causes this high pitched sound at the solenoid valve. You can adjust the water pressure a little at a time and see if it helps, just make sure you’re getting enough water across the water panel.

Maybe the hose is blocked. Take the hose off the supply side, and blow into just enough to add pressure to it and see if that works.

Try this site for more details or a similar issue:

Honeywell HE240 new install not working

Check to see if there is 24 volts at the transformer when the blower motor kicks on, if not the transformer will need to be replaced. If you do have 24 volts then work you way from the transformer toward the solenoid and see where the voltage stops, could be the humidistat.

Yes when you turn the dial on the humidistat 24 volts gets sent to the solenoid valve and it will click open and allow water to flow through it.

http://www.appliancefactoryparts.com/humidifiers/helpcenter/breakdowns/honeywell/honeywell-he360a1027.html
A breakdown diagram of parts etc above.
http://www.appliancefactoryparts.com/content/pdfs/110672-4.pdf
Shows you the HE360A.
To me it sounds like it is wired incorrectly, the solenoid should NOT get too hot at all. The PDF above shows wiring data.

Neither, even if the solenoid or humidistat stick, it should always drain properly. Is the unit mounted on the cold air return duct or the supply plenum? If it's mounted on the supply plenum, the water panel might be getting blown forward and spilling the water. High efficient furnaces also can leak water on the floor if its drain is restricted. If hum. is mounted on return duct make sure drain is clear by blowing through it. On Honeywell hum's I've seen the rubber hose from the solenoid valve to the distributor tray leak too, check the rubber 1/4" hose.

should be 2 wires going to humidifier you will connect wires from humidistat to them.

In order of probability:
1) (incorrect wiring) Make sure that humidistat is in SERIES wired with the furnace.
2) (shorted wires) Check that two wires to humidistat are not touching...use your glasses if you need them!
3) (bad humidistat) disconnect the humidistat and put an ohmmeter accoss the two terminals when it is turned on you should read 0 ohms, and when off it should read infinate ohms, if not pass both these tests, you need new humidistat.
That is it, there are no other possibilites!

Have you checked the position and function of the floats in the pan?