Controlling op amps amplification ratio by arduino
The basic principle is easy to implement.  A non-inverting configuration has a resistor Ri from the inverting input to ground, and a feedback resistor Rf from the same input to the output.  The signal is applied to the non-inverting input.  The gain is 1+Rf/Ri.  You can control the gain by changing Ri, which can be done via a CD4016 quad analog switch and 4 resistors.
HOWEVER, the Arduino is a 0-5V device.  The CD4016 can handle 15V, but to switch it the digital input must pass through half the supply.  The op-amps you mention will require bipolar supplies to handle AC signals (which I assume is what you want), so you could run them with +/-7.5V, with the CD4016 powered between them.  Then to get the Arduino 0-5V to toggle the CD4016 you'd need some level-shifting transistors to get it to +/-7.5.  The upshot is that this is surely going to be more trouble than it's worth.
However, if you are willing to drop the ancient op-amps and use a modern single-supply type (MCP6021, LT1013, etc) that runs on 0-5V, you can use input and output capacitors to convert the signal to AC, then just use the CD4016 as-is. Or JFET transistors, or even bipolars to switch the gain resistor under Arduino control if you don't need audiophile quality.