Which "omni" word describes God as having no beginning and no end?

The word is "omnipresent". It means God can be anywhere at any time, thus having no beginning and no end.

https://en.wikipedia.org/wiki/Omnipresence

God is often described as being "omniscient, omnipotent, omnipresent, and everlasting," meaning all-knowing, all-powerful, everywhere, and eternal. I don't know a synonym for "no beginning and no end" that begins with the prefix "omni-."

constant, ageless, constant, continual, deathless, durable, endless, enduring, eternal, eternity, forever, immortal, imperishable, incessant, infinite, interminable, lasting, never-ending, perdurable, perennial, perpetual, tedious, timeless, unceasing, undying, uninterrupted
http://thesaurus.reference.com/browse/everlasting

The Book of Revelation refers to him as the "Alpha and Omega," which are the first and last letters of the Greek alphabet, and the equivalent of our calling him the "A to Z."
http://bible.cc/revelation/1-8.htm

One-word answer to the question: none.

I'd go with omnipresent as it deals with inhabiting physical space without beginning or end.

Omnipresent -- adj : being present everywhere at once

Omniscient -- 1 : having infinite awareness, understanding, and insight 2 : possessed of universal or complete knowledge

Omnipotent -- adj : having unlimited power

https://www.thefreedictionary.com/omnipresent

https://www.thefreedictionary.com/omnipotent

https://www.thefreedictionary.com/omniscient