This isn't an easy situation to be put in, and it takes practice to be ready, don't give up
Also, Mormons and JWs aren't the only ones to do door knocking, a church building I used to go to (before a disagreement about Xmas set alarm bells ringing for me, I don't go anymore), I also had an odd group come to my door once claiming they were part of some kind of new testament roots movement that was trying to get back to the writings of Paul or...something like that, the two women wore veils, supposedly met in a house, but were using a New King James (a deceptive and abominable attempt at a translation).
Think about it this way, there are dozens if not hundreds of cults out there, and trying to learn even the basics of everything all of them teach will leave you with a massive headache, and there will be a new cult movement popping up soon anyway, so keep it simple. Have some form of tract on hand that explains the gospel directly and simply. If they claim to be Christian, ask how their belief is in the bible? Is it the word of God? If so, show them the ten commandments and verses that say how wicked man is, EG: in Romans 3:10 "As it is written, There is none righteous, no, not one: {3:11} There is none that understandeth, there is none that seeketh after God."
Then verses on God's judgement of sin, and how certain and final it is and how essential repentance is. If this angers them or makes them want to leave, then don't take it as a failure, think of it as scripture making a direct hit on their faith in their works, this could be the start of their journey to salvation or it could be the moment they reject Christ in order to appease their religion or their pride. Either way, you've definitely done your part to warn them and try and witness to them.
On the other hand, if they are willing to listen and show a repentant heart, (it happens but is not the usual result so rejoice if it happens but don't expect it), then you can show them share with them the good news of Christ's birth, sinless life, ministry, atonement for sin on the cross, his resurrection and his promised return.
It's good to know what kind of tactics cults and false converts use, but it's even better to know scripture and what God says, because that's the only thing that matters in the long run. Plus it's infinitely less confusing.
God bless, hope you get another opportunity soon