These units are either the common ones in the cockpit or what ATC (under the FAA) expects reporting in. Europe may report differently, but I consider the US in the "west" if you further specify where you are asking about the answer may change.
Speeds: Knots or Miles Per Hour, depends on the aircraft and the ASI installed. Some jets also use mach number.
Pressure: Inches of Mercury usually you can find this in the local ATIS. ATC (if you are entering a controlled area) will give you the altimeter setting using these units. For example you may hear "123AB Cleared to the field, Altimeter 29.91" when getting a Class C clearance
Altitude: Feet (usually 100's). When above 18,000 its usually referenced as a Flight Level. ATC expects reports in Feet when announcing altitude.
Distance: Nautical Miles or Statute Miles
Volume: US Gallons (note this is different from an imperial gallon) for fuel or pounds, depends.
Position: "X miles north of Y Location" (or something similar). GPS locations can be used. When flying IFR or on airway a location identifier may be used.
With modern glass cockpits many of these units may be configurable. These units better reflect the older standard gauges used in the US many of which may still be in service.
This FAA handbook outlines instrument layout and the like, you may want to take a look at it for deeper specs but the units included in it are listed above.