The original definition of the adjective droll is amusingly odd or whimsically comical. The word comes from the French drôle, a noun meaning buffoon or scamp, so the English word should be synonymous with buffoonish.
But some writers use droll to mean deadpan, sarcastic, muted, or dull or to describe someone with a dry sense of humor. There is no etymological basis for this, yet it is common. For example, these writers obviously don’t mean amusingly odd, whimsically comical, or buffoonish here:
I spent a lot of my time with him puzzled by how little of the Munster I was able to detect in his droll and contained Harvard bearing. [New York Times]
“[H]e finished by saying that he thanks God for the catfish because life would be droll, boring and dull if we didn’t have someone nipping at our fins.” [quoted on MTV]
Live, post-rock can sometimes feel droll and never-ending, whilst the same artist on CD can feel uplifting and euphoric. [Glasswerk.co.uk (link now dead)]
It is easy in a world where cynicism is everywhere to lose sight of the few moments of optimism that punctuates our droll existence. [The Nation (Pakistan)]
For such questionable uses of droll, alternatives such as dry, sarcastic, cynical, and wry might work better.
And these writers use droll in its more traditional sense:
It bears his hallmarks, with droll physical comedy from its animated characters and a stripped down storyline that lends itself to mime. [The Virginia Pilot]
But in most other respects this wry look at British identity through the lens of football is bang on target: droll, daft and deft. [Financial Times]
Benny Boot is a quirky, original and droll gag-write. [Chortle (link now dead)]