Heavy cav (I suppose that we are are still talking about the soul reavers ?) and heavy fliers are two different matters with their own counters.
For the fliers, I advise you to look at the following threads on the official mantic forums :
1- Reminder of the fly rule, its potential and limits, plus general tactics :
2- Exemple of an army build taking heavy fliers into account, but still a general balanced army, it's a goblin army, but the general strategy can also works very well with dwarves (replace the tromblones with flame canons and keep the general idea)
Also a general reminder : you are slow, so accept that you opponent will get the first strike, simply make sure that whatever unit he charges, you will be ready to make him pay with at worst other units charging back to avenge the fallen.
Remember that fliers (and vampires) are very expensive in points, so against an army that is using them heavily even dwarves should have the numbers advantage. If you opponent bring 2 hordes of elohis, for the same points you should be able to bring 3 hordes of elementals and still have a few points left (or other heavy hitters). Bane chant is also a great way for you to add some offensive power where it is needed the most, especially against def6+ units (soul reavers or a dragon hero with the magic armor)