Dryer won't start. Uses a 4 prong 240v outlet where hot/ground is 120v but hot/neutral is 50v. What's wrong?
It's an open neutral.

The neutral wire has lost connection somewhere. 

You are getting indeterminate readings because you are using a common digital multimeter (DVM).  Those have very high input impedance - which is normally a desired feature in a meter.  However on a long run of parallel wires, if a floating wire is near a live one, it will pick up a "ghost voltage" by capacitive coupling or induction.  It doesn't exist in any usable amount of current (paying out 500' of wire under a high-tension line won't get you anything), but these meters are so sensitive they will pick it up as a varying voltage somewhere between 0 and the line voltage of the adjacent wire(s).  It's common for it to drift around, that's a sure sign actually. 

So that tells you that your neutral break is probably not right at the receptacle. 



As a sidebar, 3-prong (groundless) NEMA 10 type connectors are still allowed for dryers and ranges. These omit ground, and ground the chassis of the machine to neutral. The logic is that these appliances are rarely moved, and neutral wire failures are extremely rare.  Not so rare, apparently.  When you lose neutral on a NEMA 10 connection, it electrifies the chassis of the machine. The washer next to it is properly grounded, touch both and BLAM.   

So that 4-prong hookup provided a real safety dividend for you today.