There can be a gentle shudder when the engine kicks on, but for the most part it should feel like nothing. The transmission is a planetary gearset, and the speed of the wheels is a ratio between how fast the engine and MG2(?) are spinning.
I'm not a Prius expert but I'm guessing if it feels like anything at all, the engine probably needs something. Spark plugs? Air filter? I know some Prius engines begin to burn oil, and I imagine that can foul plugs or an O2 sensor, possibly without immediately showing a CEL.