The words "work" and "works" have a complicated plural status. The simple definition of work includes:
work — something produced by the exercise of creative talent or expenditure of creative effort : artistic production an early work by a major writer
You can refer to these in the plural:
These works of art are masterpieces!
Or you can refer to an entire body of work at the same time:
body of work — the total output of a writer or artist (or a substantial part of it); "Picasso's work can be divided into periods"
Note that "body of work" doesn't require "body of"; the example sentence in the dictionary linked simply uses "Picasso's work".
This usage, however, is not considered plural:
Picasso's work is extremely influential.
But if you used the plural "works" you could still say:
Picasso's works are extremely influential.
These two sentences have roughly the same meaning.
To return to your actual question:
His work in research and teaching have been ...
His works in research and teaching have been...
His work in research and teaching has been ...
We can trim the sentence down to make it easier to read:
His work have been influential.
His works have been influential.
His work has been influential.
Option (1) is incorrect because this usage of "work" would refer to the "body of work" and is considered singular.
Option (2) is grammatically correct and uses "works" to refer to multiple works as noted by the definition quoted earlier: "something produced by the exercise of creative talent or expenditure of creative effort."
Option (3) is grammatically correct and uses "work" to mean "body of work" and refers to the same set of works as option (2).
Therefore, (1) is wrong and (2) and (3) mean roughly the same thing.