Take the words "strive" (lit. "agonize" or "struggle") and "narrow door" seriously. They were spoken in the middle of Jesus' travel narrative, while He was going deliberately to Jerusalem to suffer and die - so He was deadly serious. To the question "Will the saved be few?", asked by a self-confident Jew, Christ gives a command, not an answer. He explains with a caustic parable making it clear that mere knowledge of Christ does not constitute following Him (i.e. the kingdom of God). Jesus, not we ourselves, determines who gets in.
Expect a struggle. However, this does not mean that "I must do more works." For we can't fulfill the law of God! Strive instead to cling to His teachings and gifts, to oppose the devil who would have us fall and regress. Be strengthened in the Sacraments - for if He is really in you, then you are indeed able to obey God, every word. Therein, in Christ, is the door to heaven, open to us; no one on earth can lock
it. Jesus Himself is the narrow door. It's not us, it's Him.
Soli Deo gloria.