Well, here goes nothing.
My thoughts really are that someone who is genuinely, truly evil is not capable of love. When so-called "love" is motivated by self-interest--as I think all evil individuals are--then I can't call it "love." That's why I think only the second poll item is possible--Strahd can obsess over Tatyana, yearn for her, give up his mortality and soul for her, but (IMHO) he can't actually LOVE her. It's just beyond his capabilities, and pretty much always was. Maybe as a young boy he could have, or maybe not. Maybe it just slipped through his fingers one day, washed out by the river of Terg blood he shed in reclaiming his homeland.
I guess I have to define "love" as being self-sacrificing... when the happiness of someone else is more important to you than your own. I don't think evil people have the ability to feel that way--I believe they will always care more for themselves than anyone or anything else. Like Hazlik's feelings for Eleni of Toyalis--I think Gaz I states that "while Hazlik does care for Eleni, he loves himself far more." Which is of course, why he'll go through the Mulan-destruction/life-force transferral ritual.
Or, more obviously, like Strahd--he
convinced himself that Tatyana would be far happier with him than with a naive boy like Sergei, but 'taint necessarily so. His own happiness required that Tatyana love him and not marry Sergei, and he took rather violent (and final) steps to ensure that his own happiness would come about.
I think Nathan hit it on the head when he mentioned the philosopher who postulates that "evil" individuals see the rest of the world not as thinking, creative entities like themselves but as objects to be possessed or manipulated for one's own pleasure. So I don't really hold with the example of the mafia guy or the guard from Auschwitz--I think the mafioso views his children (and wife, if she's there) as his possessions... things that give him status and that other "families" will try to take away. He defends them out of pride and reputation, not because of genuine affection.
Same thing with the guy from Auschwitz--if he's a mass murderer during the day and comes home to his wife and children at night, he's still the same mass murderer. To be able to do the things he did, he had to shut off his capacity for empathy, which I think is another important ingredient for actual "love" to exist. My belief is that he is just going through the motions being affectionate to his wife and children... but he can't truly care about them (at least not the way he once could) because of what he's done.
Anyway, that's my two coppers. Thanks to everyone who provided responses--even if I don't fully agree with most of them, they certainly provided some food for thought.
yet he was a mass murderer 
but was capable of love.....
had nothing to be afraid of he tried to express his love. The fact that he did never reach the "sweetheart" part isn't because he didn't want to - it was because his love was to be turned into his torment...