Jesus explains the Old Testament's teachings on oaths (Leviticus 19:12; Numbers 30:2–4; Deuteronomy 23:21–23; Psalm 50:14; Zechariah 8:17).
The Pharisees had different levels of commitment for oaths. For example, oaths not mentioning God were less serious. Jesus teaches that everything connects to God. This includes heaven, earth, Jerusalem, my head (see also Matthew 23:16–22). So, breaking any oath disobeys God's command (see Exodus 20:7).
The main idea is to always be truthful. The teachings of Jesus make a disciple's simple "yes or no" as serious as an oath. Honest people do not need oaths (James 5:12).