By those definitions, the closest I can come to any of these is compassion.
I will listen and try to offer something useful if I think it will help, but I can't say I particularly care either way what someone decides to do or tells me. It doesn't cost me anything to listen and/or provide words that could help them resolve (or at least feel better, or even just provide a different perspective of) their situation, so if I can, I will. If that's compassion, then OK; good for me. But I don't ascribe that element of personal interest to it. I don't push people for information under the pretense of caring, because I don't. If people WANT to tell me something, I listen. If they WANT my help, I'll give it if I can. That's as far as it goes. It's their thought and their feelings, and what they choose to do about them, if anything, is their affair. If talking to me or asking me for advice is a part of that, then I'll help. I suppose it's compassion of a different kind, because I could just as easily turn them away, but it's not really personal to me; it's just another conversation. I'm not thinking their thoughts, or feeling their feelings. How could it be personal to me? All I know is what they're telling me. It's not MY problem. Involving me doesn't make it my problem either.
I can't say I'm particularly sympathetic to others, because I hate it when others are sympathetic to me. Sympathy is a waste of time. So you're miserable because I'm miserable. How does that help me feel better? Should I feel better because you're suffering on my behalf? How does this resolve things in any way? I can't just pass my problems on like that, can I? It's a twisted form of emotional martyrdom that is completely unnecessary and absolutely useless. It serves no purpose other than to make someone else feel better about your problems. I loathe it. It's one of the many reasons that I won't tell people when something is bothering me - it's quite enough that I'm bothered, thank you, I don't need sympathy.
As for empathy...well, I just find it extremely arrogant to assume you know what another person is feeling because you may have had a similar experience, so its not something I tend to show. I might, privately, think I have an idea, because I'm arrogant enough to assume these things in the space of my own mind, but I'm not going to presume I do out loud unless I'm told by the other person that I definitely know where they're coming from, and even then I'm going to take that with a pinch of salt. Suffering is not comparable.
To me, all three of these things are very selfish practices, by the definitions listed above. They aren't for the benefit of the other person, they're for YOU, and they're YOUR reaction to someone else's feelings. In trying to consider someone else's feelings, you are in fact disregarding them entirely in the face of what you want to do to resolve them, regardless of what the other person might think or feel regarding your interference. If you're willing to involve yourself in others lives emotionally in this fashion, I've always thought it better to see what someone else wants of you - if indeed they want anything at all - before you react. After all, it's none of your business unless they choose to involve you. That's just my personal opinion, though.
...yeah, I know. It's no wonder I don't have any friends, right? Haha.