busy doing / with

(a) I can't say I like this formulation. It doesn't feel natural. Although if you must use it say "doing their work"
(b) "They are busy with their work." There are specific contexts where you could use "works" but they are rather unusual.

Vincent Teo

(a) They are busy doing / to do their woek.

(b) They are busy with their works.

Sorry I wasn't clear.

(b) is fine as "They are busy with their work." I just meant that in some unusual contexts you could use "works" but that in the vast number of cases you wouldn't.

As for (a) I can't really put my finger on what seems odd about it. Possibly because you would most often hear "They are busy" as opposed to "They are busy doing their work."