How variable is a typical U.S. 110V outlet current?
The normal supply voltage at the meter is 120 volts +/-5% or 114 to 126 volts. Voltage drop between the meter to the outlet that is farthest from the meter could make the minimum voltage as low as 104 volts, but 110 volts would be more typical. Utilities in the USA usually maintain the normal voltage range quite reliably. There is data available showing typical magnitude, duration and frequency of short-term voltage surges, sags and outages.

The supply ratings for electrical and electronic devices are voltage and frequency. The current or power rating of a device is the maximum current or power that the device will take from the supply. The device determines how much current is drawn. The supply voltage can influence the current drawn, but the supply current available doesn't influence the current drawn.

Edit: By "device," I mean a product that is plugged into an outlet. Component part ratings are more complex.

Edit re outlet current ratings:

Household 120 volt circuits are rated to provide either 15 amps or 20 amps and supplied through 15 or 20 amp fuses or circuit breakers. Kitchen counter outlets and bathroom outlets are required to be supplied by 20 amp circuits. Other outlets can be connected to 15 amp circuits. Unless there is only one outlet on the circuit, any single plug-in item is not supposed to require more than 80% of the circuit rating or 12 amps for 15 amp circuits. Products that have 15 amp plugs are normally designed to take no more than 12 amps.