I find Janna to be a surprisingly strong soloer, as well. Because her tornado outranges just about everybody, she can harass and do a decent job of denying. Additionally, she has great escapability in the case of ganks, and she has great lane survivability.
I don't think tanks make particularly good soloers, mostly because they are melee and can't last hit at the same rate as ranged characters. Because of being melee, they also suffer when it comes to denying minion kills.
As far as Heimerdinger, I've found that as Teemo, I can generally take out his turrets. The best way, of course, is to AoE them to hell. It's important to remember that his turrets auto-target, and if you manage to get a minion in range of his turrets first, you should be able to get a few hits in on the turret, killing it. If you do this a couple of times, you'll get the hang of obliterating Heimer's turrets.
It's important to note, as relates to this thread, that no jungling character should be soloing mid. If there are characters that are not effective junglers compared to your Yi or Nunu who called mid, the latter should be jungling while the former should be soloing.