Pretty much anyone who has decent ranged ability to kill turrets and some kind of AoE to counterpush can stop Heimer. Karthus, Sivir, Galio, Malzahar, Cho'gath, Gragas, and Caitlyn can all do it.
Jax can get rocked by AP burst with DFG, since Jax players tend to skimp on actual defensive items besides dodge boots in favor of stacking more HP through damage. A Vayne packing SoTD with a properly executed Condemn stun can do well, as can Kog'maw with SoTD. Champs with attack speed debuffs are also pretty good picks, like Nasus, Malphite, and Gragas.
Pick any decent assassin to kill Kog'maw. LeBlanc and Kassadin are two good picks that aren't banned too often because everyone bans Jax/Akali/Rammus/Shaco/Poppy.