The word translated as "strait" in the King James Version is στενός. The word appears only in the verses of Matthew you cite and in Luke's parallel version (13:24). Some examples from the Septuagint are (following Brenton's translation, translation of στενός in bold):
Numbers 22:26 LXX
And the angel of the Lord went farther, and came and stood in a narrow place where it was impossible to turn to the right or the left.
1 Kingdoms 23:14 LXX (MT: 1 Samuel)
So David swore to Saul: and Saul departed to his place, and David and his men went up to the strong-hold of Messera.
2 Kingdoms 24:14 LXX (MT: 2 Samuel)
And David said to Gad, On every side I am much straitened: let me fall now into the hands of the Lord, for his compassions are very
many; and let me not fall into the hands of man.
1 Chronicles 21:13 LXX
And David said to Gad, They are very hard for me, even all the three: let me fall now into the hands of the Lord, for his mercies are
very abundant, and let me not fall by any means into the hands of
Judith 4:7 LXX
... charging them to keep the passages of the hill country: for by them there was an entrance into Judea, and it was easy to stop them
that would come up, because the passage was strait, for two men at
Isaiah 30:20 LXX
And though the Lord shall give you the bread of affliction and scant water, yet they that cause thee to err shall no more at all draw nigh to thee; for thine eyes shall see those that cause thee to
The phrase translated as "narrow is the way" in the King James Version literally says "straightened is the way", using a participle of the verb θλίβω, which means something like "to experience trouble". Examples elsewhere in the New Testament:
And he spake to his disciples, that a small ship should wait on him because of the multitude, lest they should throng [press] him.
2 Corinthians 1:6
And whether we be afflicted, it is for your consolation and salvation, which is effectual in the enduring of the same sufferings
which we also suffer: or whether we be comforted, it is for your
consolation and salvation.
2 Corinthians 4:8
We are troubled on every side, yet not distressed; we are perplexed, but not in despair
1 Thessalonians 3:4
For verily, when we were with you, we told you before that we should suffer tribulation; even as it came to pass, and ye know.
Thus, when we look at how these two words are used in other passages, the image is one of intense struggle - something a little stronger than "strait" and "narrow". A better translation might be: How narrow the gate and how hard the way which leadeth unto life.
The Byzantine (Greek) commenter Theophylact explains this passage thus:
The narrow gate means both trials that are voluntarily undertaken,
such as fasting and the like, and trials that are involuntarily
experienced, such as imprisonment and persecution. Just as a man who
is fat, or who is carrying a great load, cannot go in through a narrow
gate, neither can a gourmandizer or rich man. These go in through the
wide gate. To show that narrowness is temporary and that the width is
likewise transitory, He calls them a "gate" and a "way". For the gate
is hardship, and he who undergoes hardship passes through his hardship
as quickly as he would pass through a gate. And the pleasures of the
gourmandizer's feast are as transitory as any moment in a journey
along a road. Since both are temporary, we ought to choose the better
of the two.
Explanation of the Gospel According to Matthew (tr. Chrysostom Press, 1992), p.65