Op Amp output's noise changes when the gain changes
The oscillation is a result of instability in the layout, perhaps inductive power or ground leads without decoupling ’s on power to gnd .

Unity gain gives the widest BW (from fixed GBW) but also the lowest phase margin which degrades with any capacitive load, unless compensated with reduced BW.

There is also a slope on the pulses, which suggests another reactive effect in your layout not shown on your schematic but could be uncalibrated 10:1 probe error. 

So correct that with the probe trimmer and scope test pulse , add ceramic caps. to both supply rails and use a very short probe ground lead to get textbook waveforms from DAC then OpAmp.

Even Alkaline batteries make random noise which you can hear with 1.5V on a speaker, spurious effects depend on the phase margin which can improve with gain or in your case be asymmetric while improving.  

Define your capacitive load! Is there a long cable output and measure your 9V supplies with a divider.