Kazakhstan is blocking some websites, including home pages for Tor and popular VPN services. Also it uses some sophisticated Tor blocking: it establishes TCP connection but no bytes going there, so Tor client just hangs there without error or traffic, I wasn't able to unblock it, though I did not try hard enough. I think that they are blocking connections to popular VPN services as well, but I don't really know. Without access to their home pages it's hard to connect anyway. I know that people successfully using some mobile apps as VPNs, so while they are trying to block VPN, they are not trying hard enough.

I never had any problems with SSH and I operate my own OpenVPN on VPS using standard port and I never had any problems with it as well.