This passage occurs in the Epiphany season of the Revised Common Lectionary (Year A), most recently February 2017.
I updated this a fair amount in 2017.
The basic meaning of the passage should not be lost: Discipleship of Jesus means living our lives in contrast to the world's general order. This might invite the preacher to lean heavily on the law for such a sermon. A closer examination of verses 18-20 suggests that Jesus clearly rejects the law as a path to salvation. First, those who don't do law are still in the kingdom of heaven; second, those who love the law do not have the necessary righteousness and finally, the law eventually will give way in the new creation.
μωρανθη ("lost flavor" or "made fools," aorist passive subjunctive of μωραινω, 5:13): The word here means "lose flavor" but elsewhere means "make fools." Paul uses this saying that people, thinking they are wise, have become fools (Romans 1:22; 1 Cor 1:20). Interesting to think about salt (ie, us) becoming fools! Maybe this is precisely the call of the beatitudes and the sermon on the mount: We are to become beaten down by the world, trampled underfoot. Our hope is not in the world's kindness, but the power of Christ's resurrection to renew and restore us.
ορος ("mountain" or "hill", 5:14). A small reminder that this passage takes place during the sermon on the mount! In another blog post I look at how Matthew uses mountains.
λαμπει ("shine," of λαμπω, 5:15; also 5:16; also 17:2, during transfiguration). The only time anyone truly shines in the Gospel of Matthew is Jesus during the transfiguration. A reminder that the church only functions as the light when it reflects the light of Christ.
νομισητε ("think," aorist subjunctive of νομιζω, 5:17). Jesus kind of does a play on words here. He says that he has not come to abolish the law (νομος). He starts out the sentence with a verb that has the same root. Okay, nothing here for a sermon, more a little smile when you read the Greek :-)
ιωτα ("iota," 5:18). This is fascinating. The law here has already been translated from Hebrew to Greek. The tiddle of Hebrew has been changed. Yet Jesus argues that even the smallest point of the law remains. So do we assume here that this means the law is so eternal that it transcends language?
εως ("until," 5:18). It is worth stopping for a second here -- until heaven and earth pass away, the law remains in power. This suggests that the law is incredibly enduring, yet not eternal. It too shall pass away. It is worth remembering that the law was given to deal with sin (Galatians 3:19). Once sin is gone, no more need for the law. However, we will not get rid of sin until heaven and earth pass away and therefore, the law is with us.
ποιηση ("do" aorist subjunctive of ποιεω, 5:19): Alas my Lutheran heart sinks. Jesus actually expects us to do stuff. It is fascinating to look up the word faith in the Gospel of Matthew. Faith leads to sins being forgiven (9:2), heals people (9:22; 9:29; 13:58; 15:28), moves mountains (17:20), empowers prayer (21:22). So it is not that faith and justification are separate in Matthew's Gospel.; rather, Jesus expects people to do stuff!
δικαιοσυνη ("righteousness"; 5:20) If the Pharisees and teachers of the law have not achieved enough righteousness before the law to get into the Kingdom of Heaven, what hope do we all have? Practically, I think Jesus reminds us that observation of the law is not just about the letter, but also the Spirit (which the Pharisees miss). Existentially and ultimately, this verse, like so many others in Scripture, reveals that our righteousness before the law is not what gets us into heaven. Even the most law observing people cannot achieve righteousness. However, Jesus said in the verse prior that people who don't do the right things are the least in the Kingdom. So we need a righteousness that exceeds the most moral of people to get in; yet the least moral get in. Clearly, righteousness before the heavenly throne is not based on the law.
Grammar review: How to translate the aorist subjunctive
As you can tell from the words above, Greek likes to employ the aorist subjunctive. This is both complex yet simple for the English reader. It is complex because it is used in many and unusual ways. "Subjunctive" normally refers to hypothetical events. However, Greek conceives of the subjunctive in some different ways than English. So understanding what is signified by the aorist subjunctive may not be very intuitive or directly translatable. What makes it simple is that there are basically six (or so) categories of use and they all have a translation formula. This passage has a most of the categories for translation.
In 5:13, you have the aorist subjunctive in εαν clause: μωρανθη
The word εαν signifies an uncertain event (technically ει αν) and will almost certainly have a verb in the subjunctive mood. In this case, Jesus is saying that the salt may or may not lose its flavor. The way to translate this is with the word "if." If salt loses its flavor...
εαν + μη or ει + μη clause
In 5:20 you have this in εαν μη περισσευση. The way to translate this is with "unless"
ος αν clause
This is akin to εαν in terms of hypothetical translations. In 5:19 you have this with ποιηση, when its used with ος αν. In this case you can translate it with, "whoever"
5:17 reads μη νομισητε. Greek will put simple commands in the μη + aorist subjunctive. This implies that the listener should do this activity without implication of the action being on-going. You could think of this as a prohibition. It is how Greek does negative aorist prohibitions. Like "Don't eat that" would employ aorist subjunctive. In contrast, when Jesus says, for example, "Do not let your hearts be troubled," he uses the present tense, implying that they were worrying and they shouldn't ever again. The way you translate this use of the aorist subjunctive is by saying, "Do not XYZ." Aorist subjunctive makes no implication about past or future action.
ου μη prohibition
5:20 ου μη εισελθητε. This simply should be translated as "no, not ever" Strongest negative possible in Greek!