First, select the table and click Table > AutoFit > Fixed Column Width. That
prevents the columns from expanding the width.

Then, with the whole table selected, go to Table > Table Properties > Row.
Check the box for "Specify height". Set the amount of vertical space you
want to allow, and change the right-hand dropdown to "Exactly".

If users insert more text than will fit in a cell, or press Enter too many
times, the extra text will just disappear below the bottom of the cell. It
will really still be in the document, just not visible.

Also, unless the document is protected for forms or for comments, the users
will be able to drag the table's borders to change the cell size. They would
have to do that deliberately, though.