Since they seem to be making the rounds quite frequently, I would like some advice on how to interact with them. Do I just take the pamphlet and let them go on their way? I really don't want their literature in my house, but I guess I could immediately put it in the recycle bin. Or, should I feel obligated to interact with them in the hope of sharing a bit of the true Christian faith?
I wouldn't say you should feel obligated to interact with them in order to share the faith--it really depends on how well you know your faith, IMO. I will usually open the door and talk to them, but will not usually invite them in. I let them do their routine and something they say is usually enough for me to ask a question and then share the Orthodox perspective on whatever it is. Most of the time, they're not interested in another perspective enough to stand at the door and discuss it--they'd rather come in and talk in my experience. Once I had an extended discussion with a JW while in flight, which was pleasant: we talked about the Name of God, why they insist on Jehovah, etc. Talking with them can be nice; you may not convert anyone, but sowing a seed is not a bad thing. But be prepared, because it's not always so nice.
I have a cousin who invited a JW at the door into her home and that started a series of "Bible studies". Her mom is more Orthodox than she is, but even with her there to answer some of their challenges, they were stumped, so they asked me to meet with her. She was a very pleasant lady in her late fifties or early sixties. Somehow, we started talking about/debating the divinity of Christ, and I pointed out their peculiar (mis)translation of John 1.1, opened my Greek NT and began translating and exegeting on the spot (the Greek threw her off, I don't think they really look at anything other than their New World Translation), consulting other passages, etc. I put the question to her "Is Jesus divine?" and she answered without any hesitation, with full confidence, and looking me straight in the eye, "Jesus is not God, he's God's son; Jehovah created him", and regarding the Holy Spirit, "The Spirit is a force, a power of God, it's not God or a person". Now, I already knew that their "Christology" was basically Arian, that they rejected the divinity of the Spirit, and so on. But, in all honesty and without any intention of exaggerating, something about the way she said those things hit me like a ton of bricks: I felt a chill, my stomach turned, and my aunt says my face became pale. I've met plenty of people who were confused by Trinitarian theology or Christology, but this was different somehow, and I wasn't expecting to react in this way. We finished our discussion, she left, and I became very quiet, I didn't feel like talking to anyone (though I did ask for some milk and a whole package of Oreos). I didn't feel right for a few days after that. I don't think the lady was evil, but it's the closest thing I've experienced to I Jn 4.1-3 in my life.
You could always ask them to pray with you. I did an extemporaneous prayer with them once and started invoking the Mother of God and various saints; that freaked them out.