OPA2340: Step response abnormal oscillation

Harson,

What you describe is not an oscillation but a known recovery time required after driving the output into a rail.  Even though the input common-mode voltage is literally rail-to-rail, output cannot follow all the way to neither rail.  And attempting to drive the output to either rail will triode one of the output transistors and result in collapse of one of the internal nodes inside the output stage.  As the output is then driven away from the rail, it takes the collapsed node around 5us to fully recovery from the non-linear condition culminating in the burst of noise you see on your scope picture as the node settles on its final value.

The best way to prevent this condition is NOT to drive the output closer to the rail than specified in the data sheet. Another way is to add a pull down resistor from the output to an additional negative supply in such a way as to sink the quiescent as well as any possible load current. By doing so, the transistor in the output stage does not have to carry any current allowing the output to reach the rail while maintaining its linear operation.

OPAx340 is a twenty year old rail-to-rail output op amp designed using a different output stage topology that can drive very large capacitive loads but it's proned to overload recovery problems discussed here. All other op amps mentioned by you are less than ten year old and use a different output stage - Monticelli Class AB output stage - that was under patent protection at the time of the introduction of OPAx340. Monticelli output stage cannot drive as much of capacitive load but it does not suffer from the kind of delayed overload recovery time discussed here.