If you exert force on an object and the object does not move, is any work done?

Nope.
Work done is force x distance moved due to force -

https://en.wikipedia.org/wiki/Work_(physics)

So even if force is a HUGE number if distance = 0 then the answer = 0.

In physics no work is done.

However, when work is considered manuel labor then yes a person is exerting their muscle strength which is a work situation.

https://en.wikipedia.org/wiki/Manual_labour

If the Object Doesn't Move -- Work is not always force x distance, but work always involves motion of some sort. No distance - no work.

Work is NOT Force!

Many beginning physicists confuse "exerting a force" with "doing work." As seen above, you have to change the kinetic energy of an object in order to do work on it - just pushing on it isn't enough. Even the fact that you may get tired - even exhausted - holding a heavy box or pushing on a wall, if the kinetic energy of the box or the wall doesn't change, you didn't do work. "Exerting a force" is NOT the same as "doing work!"

http://www.batesville.k12.in.us/physics/PhyNet/Mechanics/Energy/Work.html

Yes.

Since the object does not move no external work is done, as doublemm correctly points out.

However, if there is exertion without movement then your muscles are contracting isometrically (which sounds a bit weird - "contracting at the same length" - but that's the correct term). Then we have the following:

"In isometric contraction there is no external shortening of the muscle and therefore the external work done (force x distance moved) is zero. Yet sustained isometric contraction is associated with fatigue, indicating that the contraction requires continuous energy expenditure. The energy is utilized for doing 'internal work' i.e. for stretching the SEC [series elastic component]".

http://books.google.co.uk/books?id=zFl7y5xqHj4C&lpg=PA113&pg=PA113

star_gazer has this right, too.