Best JavaScript Coding Structure Using Object Literal?

This doesn't make much sense. There is no "Object Literal" design pattern, and "Object Literal" isn't a component.

Object literals (plural) are an inherent feature of Javascript syntax, and I don't see what relevance they have to any design pattern in particular or, in fact, design as a whole.

(Also, try not to worry too much about what patterns other people are using at any given arbitrary point in time. Just use the right tool for the job.)

The module pattern can be nice for certain things, but you should really consider whether you really need your properties to be private. If it is really necessary to make your properties private, then by all means, use the Module pattern:

var namespace = (function(){ 
  var a = {
    internalFunction: function (number) {/*Do internal stuff*/},
    internalVariable: 365,
    publicFunction: function() { return internalFunction(internalVariable) },
  }
  return {
    publicFunction: a.publicFunction
  }
}();

If you don't mind all of your functions being accessible, just use this simpler form:

var namespace = {
  noLongerInternalFunction: function(number) {/*Do stuff*/},
  noLongerInternalVariable: 365,
  stillPublicFunction: function() { 
    return noLongerInternalFunction(noLongerInternalVariable); 
  }
}