The two words can overlap, but fundamentally they are different.
The relevant meanings, from the OED are:
seduce, 2. In wider sense: To lead (a person) astray in conduct or belief; to draw away from the right or intended course of action to or into a wrong one; to tempt, entice, or beguile to do something wrong, foolish, or unintended.
sway, 12. trans. To cause (a person, his actions, conduct, or thoughts) to be directed one way or another; to have weight or influence with (a person) in his decisions, etc.
So, they were swayed by the low cost of the house simply says that the cost was the factor (or the main factor) which led them to reach their decision, with an implication that they were leaning towards a different choice. They were seduced by the low cost of the house implies not just that the cost changed their minds, but that it led them to make a bad choice in some sense: dishonest, or disloyal, or not keeping their word, or perhaps just not in their own best interests.
In your second pair of sentences, where there is no particular choice implied, seduce implies a physical (and probably sexual) surrender, while sway does not really make sense: I would take it to mean that there was some specific choice which hadn't been mentioned.