It also helps to obtain the material during the cool part of the year, from late Fall to early Spring, because the sap has stopped running and this makes drying it easier.
I obtain my blocks from a local wood mill, rummaging through their scrap bins. I look for heart wood and it must be absolutely perfect - no knotholes, cracks, splits, etc.
Blocks are strong enough if you pick the right material. I test each club before the final sanding and staining on a tire pell. I've tested a few on sheep skulls. I've yet to break one. Remember, baseball bats and sledgehammer handles aren't made from root balls and they're plenty strong enough.
And these clubs aren't made for busting concrete; they are made for busting skulls and bones.
The oak club seen in this thread is ferocious. It's the longest war club I've made and it has a full two handed grip on it.
Suggested woods:
Oak
Cherry
Maple
Ash
Hickory
Hornbeam
Osage Orange
Locust
Black Gum
Walnut would make a pretty club but I'm not so sure about the strength factor. I'm also curious about making one from Sycamore, as it is a good dense wood.