If an input exceeds the power supply rails on the OP4177, are there clamping diodes that will protect the device? If so, how much current is allowable?
There are no input clamping diodes on the OP4177, however the internal protective circuitry will allow you to go to 2.5V beyond the supplies. If you expect the input to go farther than 2.5V, you can use an additional series resistor at the inputs to limit the current going into the device. For the OP4177, limit the input current to within 5mA.
You can use input series resistors as high as 5kohm without severely adding to the input offset voltage. There is more information on p.15 of the datasheet. Please see the Input Overvoltage Protection section.
I can provide more help if you give more details about your application. How are you using the OP4177 and what voltages are you expecting at your inputs?