you seem to have installed your DC input where your bulk capacitance should live, and now that i look at it, your 0.1uF ceramic should have probably been put a whole lot closer to the op amp, so its very possible a good bit of noise off your supply is being coupled in, the oscillation spikes are about 240Hz, which would line up roughly with a double of the 120Hz ripple being spat out by a cheap wall wart,