Does a vow take effect merely by intention and uttering the word to oneself, without speaking it aloud, or does a vow only take effect if a person speaks it to himself but does not intend the vow?

A vow is not binding if it is merely a thought or if it is expressed in a form that does not convey commitment. The binding form is: "It is a duty upon me for Allah that I do such-and-such an act of obedience." Therefore, what you mentioned does not obligate you to anything. One should beware of falling into obsessive thoughts. Furthermore, making vows is disliked, due to the prohibition of the Prophet (peace be upon him) against it, for it does not bring forth any good but rather extracts from the miserly.