Трябва да използвате req.params.user_id
вместо req.body.user_id
exports.updateUser = function (req, res) {
console.log(req.body);
User.findByIdAndUpdate(req.params.user_id,{$set:req.body},{new:true}, function(err, result){
if(err){
console.log(err);
}
console.log("RESULT: " + result);
res.send('Done')
});
};