Why would "Cammy" accelerate roughly only when the fueled engine is running? on 2009 Toyota Camry Hybrid

Started one morning on the freeway with no evident cause or trigger. The turbulence only occurs while accelerating when the gas-fueled part of the engine is running. Noticed when I got home that there was a wind-strewn mess of a gray, greasy gelatinous (fluid?) On the bottom,back of the engine by the axle and right-side control arm. Have any ideas what (if any at all) part/parts could've caused this?

Asked by for the 2009 Toyota Camry Hybrid