1N4148 not giving correct voltage drop
Actually it sounds like you're getting about what you should.  The voltage drop accross a diode is a non-linear function of current.  It is not a fixed voltage source, but is around 600-700 mV for most normal currents.  If the only load thru the diode is a voltmeter, which are designed to draw as little current as possible, it may look like the drop is only 200 mV or so.  You are seeing 420 mV drop, which is certainly plausible for some small amounts of current.

The basic problem is that you are trying to use a forward biased diode as a fixed voltage source.  That does work in some cases when the situation is well enough known or controlled, but this is not the best way to achieve what you want.  What you do want is a linear regulator.  There are many to chose from, but something like the 3.3 V version of the MCP1700 is a cheap chip that would supply a few 100 mA and should work for your case.

Another issue is that your USB voltage is high.  I don't remember the exact full range of valid USB voltage as can be seen by a device, but 5.42 V sounds out of spec.  Still, most 3.3 V fixed linear regulators, including the MCP 1700, will be fine with that.