EDIT: Glen_Geek thank you for your answer it was helpful.
I didn't add many details originally because I was looking for general things that could cause those oscillations, and to determine if those were the classic "oscillations" that are problems with op-amps. However, I can add more details now.
I believe the problem was a capacitive load, and I was able to remove the majority of oscillations by adding a 50 ohm isolation resistor and limiting the bias voltage applied, especially to one polarity, i.e biasing it with +2V/-7V removes oscillations and still passes negative polarity signals unaltered. I did add bypass capacitors but this did not seem to do much.
Moving on past this, I am struggling to set the gain as I wish. For simple testing I am using a function generator as the input with an impedance of 50 ohms, and simply producing a 1 MHz sine wave. The circuit I am using is this (not shown are two bypass capacitors in parallel of .1 uF and .01 uF for each bias pin):
R1 alters the output but not as expected fully. When R1 is equal to 820 ohms again, I observe a signal. When R1 is equal to 50 ohms, I observe a signal ~10X larger.I tried multiple resistors for R1 between 50 ohm and 820 ohm (200, 330, 560, 670 ohm) and all yielded the same severely attenuated signal (changing the resistor does not alter the signal). In fact, this signal is the same as when R1 is removed. Interestingly, the amplitude of this signal increases when the frequency of it increases too. I am using an LM6181 op-amp and implementing this circuit with a breadboard with the actual setup is shown below.
What could be causing these problems such that only 50 ohm and 820 ohm resistors produce an output? I also tried a different signal source, using a silicon photomultiplier (essentially a photodiode) that to my knowledge does not have exactly a 50 ohm output impedance and observed the same effects. I'd add more pictures but I can only have two links, sorry!