Does "oath" have an implied religious connotation?

Solution 1:

I would say yes. There is, at very least, a tacit religious appeal. The idea of a secular promise is a very recent idea in human history. Almost all promises of a certain importance were attached to an appeal the deity. Taking an oath or swearing to something or other does have a religious connotation. Now, some may choose not to see it that way, and legally it might not be any different that a simple affirmation of truth, but the religious connection is still there.

Solution 2:

No, it means you "swear" to do something. You can include religion to the oath, but you do not have to.

Dictionary.reference.com

Solution 3:

The US Constitution makes the distinction between oath and affirmation, the former being religious in nature, to emphasize that either an oath or an affirmation is necessary to hold office.

The Devil's Dictionary yields the following definition:

OATH, n. In law, a solemn appeal to the Deity, made binding upon the conscience by a penalty for perjury.

Solution 4:

Yes, there is an implication that an oath is religious, especially if it starts "I swear by Almighty God that...", but take for example section 4(2) of the UK Oaths Act 1978 (consolidating earlier Acts)

Where an oath has been duly administered and taken, the fact that the person to whom it was administered had, at the time of taking it, no religious belief, shall not for any purpose affect the validity of the oath.

Like most other countries, there is also provision for affirmation, in section 5(1)

Any person who objects to being sworn shall be permitted to make his solemn affirmation instead of taking an oath.