What is a non-denominational church? Some Christians claim a non-denominational church is better. However, as a scientist I like to see all angles of the story:

I was under the impression that since all Christians don't belong to one church,
(They agree to disagree on Ephesians 4 and opt for the Nicene Creed) then
all Christians doctrines are denominations - there by:
1c penny doctrine,
5c nickel doctrine,
10c dime doctrine,
25c quarter doctrine,
50c half-dollar doctrine, etc
= 1.00 dollar Eph 4 Church - some claim all Christians are part of the universal church.

I like the idea that non-denominational churches reject the idea of a denominational
structure and opt for autonomous churches. This is similar to Paul when he opted not take
money from the Corinthians but still claimed to have authority over them.

Maybe that is what non-denominational is, that there is no central government and only Christ is the head or leader?

So if non-denominational or denominational has nothing to do with doctrine. That begs the question: What is the definition of the One Doctrine in Eph 4?

Or, simply explain: What is a non-denominational church?
A non-denominational church is exactly what it sounds like.  It is a Church that doesn't adhere to any earthly authority other than maybe the local Pastor at that Church.  It doesn't recognize any denominational authority, just that of God and His Word.

I'd like to also address this portion of your question as well:


  I was under the impression that since all Christians don't belong to
  one church, (They agree to disagree on Ephesians 4 and opt for the Nicene Creed) then all Christians doctrines are denominations
  - there by: 1c penny doctrine, 5c nickel doctrine, 10c dime doctrine, 25c quarter doctrine, 50c half-dollar doctrine,
  etc
  = 1.00 dollar Eph 4 Church - some claim all Christians are part of the universal church.


Most Christians understand the universal Church to be the body of all saved Christians, period. It has nothing to do with denominations.  

From Gotquestions.org


  The universal church is the name given to the church worldwide. In
  this case the idea of the church is not so much the assembly itself
  but those constituting the church.


See also A Study of the Nature and Meaning of Jesus' Church: Universal and Local


  A. The Church (Universal) Is the Body of All Saved People Everywhere.
  
  It includes all those who have been redeemed by Jesus' blood, have
  received forgiveness of their sins, and have been born spiritually
  into His family.


In fact, it's recognized that within any given denomination, there are likely saved and unsaved people, so not all Baptists, for example, belong to the Universal Church, but some do and so on.

This can be represented with a really crude drawing (Sorry about the quality. the only graphics program I have on this PC is MS Paint.)  



The large circle represents the Universal Church, and the little ones, the individual denominations and non-denominational churches.  Bear in mind that according to the doctrine of Sola Fide, it's also possible for someone to be saved, and therefore also a member of the Universal Church without belonging to any earthly Church.

As for the One Doctrine...

If the definition of "Universal Church" is what I say above, then the "one true doctrine" is the "right" doctrine about Christ. By definition, it would be the doctrine that separates true Christians from false.  It is what defines "who are the real Christians?", which means it exists out there in the real world, but is not answerable on this particular site.