What is IP squat space
Space that someone uses to number their networks even though it is either allocated to someone else or may be allocated to someone else in the future.
"squat space" is generally not routed on the public internet by the squatter. Doing so would be considered a hijack which is a much more serious matter. Instead it is generally used behind a network address translator or for stuff that doesn't need to communicate directly with the Internet.
In the past if an unallocated range was widely squatted on the allocation authorities would hold back on making allocations from that block. However with the IPv4 address crunch this is no longer possible.
It is owned by DoD, is this space routable?
It is routable on the public Internet if the DoD wants to, but as far as I can tell it is not currently routed on the public Internet.
There is a graph showing how much of each /8 is advertised at https://ipv4.potaroo.net/fig05.png , unfortunately it's a bit tricky to interpret because some of the strips seem to be two pixels wide and others three but it doesn't look like any addresses from those blocks are advertised on the internet.
Can an expert explain to me why someone is using this range internally
Some organizations run out of private space internally, either because they weren't stingy enough with their internal allocation policies or because they are just so freaking big that private space doesn't cover their needs.
Others just do it out of ignorance, they don't understand how IP addressing works, so they just make something up.
Still others squat because they are trying to avoid their private network conflicting with customers private networks. This often comes up with things like VPN services.
and what the consequences would be?
It means that if/when the legitimate owners of that IP space start using it on the Internet their services will be unreachable for the squatter and the squatters customers.
I ran into this for a while with a server I run. The server has an address in 188.8.131.52/8 which was widely squatted on in the past. Notably by Hamachi and by T-Mobile USA. Things did seem to improve over time, Hamachi moved to squatting on a different network, I'm not 100% sure what happened on the T-Mobile side but I stopped seeing complaints coming from there so presumably they did something.