Hello,
An opinion:
One nuance. Because "funny" can mean comical, if we want to use "funny" to mean "strange" when describing a person, we might say "a little funny" which connotes that something is not right.
So: 1) He's funny. This would say he has a good sense of humor, tells good jokes, etc.
2) He's a little funny. This would suggest that the person is strange in some way.
1) That situation was funny. Suggests a good time, humorous.
2) That situation was a little funny. Maybe it was humorous,maybe it was weird. Depends on tone and context.
Another nuance: For senses like smell, hearing, taste, feel in American English we say that something smells/feels/tastes/sounds funny to mean that something is not right. This milk tastes funny. The audio on the TV sounds funny. This cushion on the sofa feel funny.
Hope that helps. I expect you'll hear other opinions and thoughts, too.
Best,
Martha