What term describes something that is amusingly odd or whimsical?

The term that best describes something amusingly odd or whimsical is "droll." This word specifically conveys a sense of humor that is quirky or dryly amusing. When something is referred to as droll, it often carries an implication of playful absurdity or a charming peculiarity that can elicit a smile or chuckle.

In contrast, "eccentric" describes behavior or characteristics that are unconventional or deviating from the norm, but it does not necessarily imply a humorous aspect. "Dereliction" refers to the act of neglecting duties or responsibilities, which is unrelated to amusement or whimsy. "Demagogue" describes a political leader who seeks support by appealing to popular desires and prejudices rather than using rational argument, and it does not capture the playful or whimsical nature encapsulated in the idea of drollness. Thus, "droll" is the most fitting choice that aligns with the description of being amusingly odd or whimsical.