3 textboxes with multiple value combinations to one output
If I understand correctly, you want to add up all the fields, and print the result. If this is the case, you are complicating things quite a lot. If you think of the problem in terms transformations it will be easier to reason about. You have a list of numbers that you want to add up, that's the problem at hand; the boolean logic expressions are not necessary, because zero doesn't add anything (it's an identity element), and addition is commutative. To prevent non-numbers from being entered, you'd check for NaN, and return identity (zero) if it is not a number, effectively doing nothing:

function sum() {
  var result = document.getElementById('result')
  var ids = ['Text1','Text2','Text3']
  result.textContent = ids
    .map(function(id) {
      // + casts a number from a string
      var n = +document.getElementById(id).value
      return isNaN(n) ? 0 : n // identity
    })
    // add up all numbers
    .reduce(function(x, y){return x + y})
}


Ideally you'd also cache the elements to not query them each time the function runs, but I doubt it would make a big difference in this case.

Demo: http://codepen.io/anon/pen/JIwHx