If you want to walk the strait and narrow when it comes to proper English, you had better write "strait and narrow" and not "straight and narrow."
Strait and straight are not different spellings of the same word but two completely different words. Strait, when used as an adjective, means narrow or confining. As a noun, it means a narrow passage of water connecting two large bodies of water, such as the Strait of Gibraltar. Straight refers to the shortest distance between two points. According to the Oxford Dictionary of Word Histories, straight was once the past participle of stretch until it was converted from a verb into an adjective. If you stretch a curly rubber band it becomes straight. Strait, on the other hand, comes from the Latin word strictus, meaning "drawn tight."
"Straight and narrow" actually makes sense and may even seem preferable to the more redundant "strait and narrow." It suggests moving ahead without detour or distraction, which is often close to what we mean when we use the phrase. That phrase, however, comes to us from the Bible (Matt. 7:14), where Jesus says, "Because strait is the gate, and narrow is the way which leadeth unto life, and few there be that find it." In other words, it's a tight squeeze, sort of like that camel trying to get through the eye of a needle that Jesus mentions elsewhere.
Proper uses of strait include strait-laced (those laced corsets make one's waist more narrow), straitjacket (confining) and dire straits. Use straight in straight razor, straight man, straight shooter, straight off and straight whiskey (even if it can make one tight).
The two words straighten and straiten are also distinct and easy to confuse. The former means "to make straight," the latter "to make narrow." Sometimes, as when stretching a rubber band, either word will do.