Why are all of my appliances becoming energized when ground wire is excluded?
It is unlikely that the chassis is getting "energized" for multiple reasons. First of all, if it was grounded the breaker would trip. Secondly, the power draw of a washing machine would be very dangerous if you touched it. Also, the design of such devices is done to make such accidents rare, otherwise the manufacturers would be facing hundreds of lawsuits. That you see the same thing in multiple appliances makes it improbable that it is current leak. (What is the probability that ALL your appliances have a dangerous current leak? Negligible.)

If you are convinced there is a current leak, it is easy to test. Just touch one end of a voltmeter to the "energized" chassis and the other to a ground. If it reads 240 volts, its energized. According to another post the OP apparently did this test and it turned out negative, confirming there is no hot chassis here, it is static electricity.

The shock is probably due to static electricity. Both washing machines and air compressors will build up very strong static electricity charges due to rotary motion. If this is not discharged by a ground, static electricity will accumulate and charge up any metal on the device. You also see this same effect on cheap, ungrounded shop vac-type vacuum cleaners.