Let's break these numbers down, ok?
20 Hz means that those birds hit the tree up to 20 times per second: an AK-47 - aka Kalashnikov - shoots 10 rounds per second, the Giant Hummingbird's wings beat rate is of 10-15 per second (see).
7m/s means that those birds' head hits the tree at a speed up to 25.2km/h (or 15.5mph). Not much? Well, dear human reader, try to run at your full speed into a tree and see how you like it... Oh, and consider also this: when Usain Bolt smashed the 100 meters world record in 2009 with his astonishing 9.58 seconds, well, he ran at 37.6km/h (23,4mph).
As for the 1200g deceleration, well, just think of this: when astronauts take off for space, they suffer an acceleration of about 3.2g, and on reentry the deceleration is about 1.4g (see), meaning that some of the fittest human beings in the world, while performing one of the most stressful procedure of 'em all, endure a deceleration 857 times lower than the one experimented by woodpeckers' head on a daily basis.
In spite of that, though, this birds' brain doesn't become like a triumph of mashed potatoes.
Well, researchers say (P) that it depends, among other things, on the fact that woodpeckers skull bones are stiffer than those of other birds, as they've "small but uniform level of closed porosity, a higher degree of mineralization, and a higher cortical to skull bone ratio" (P). Moreover, woodpeckers have an "unusual shape of the elongated tongue, also called the hyoid apparatus" which probably helps in absorbing the impacts energy (P).
But this dumb blog has a much simpler and more elegant explanation for all of this: see the following cartoon.
|Woodpeckers' brain secret (by @sciencemug)|
[Woodpecker free pic by Bill Pennell (source: Unplash); adapted by @sciencemug]
Wanna see a cool slow-motion vid of a woodpecker banging its beak+head onto a tree? Check this out!
Jung, J.-Y., Pissarenko, A., Yaraghi, N.A., Naleway, S.E., Kisailus, D., Meyers, M.A., and McKittrick, J. (2018). A comparative analysis of the avian skull: Woodpeckers and chickens. Journal of the Mechanical Behavior of Biomedical Materials 84, 273–280.