Best practices for encrypting continuous/small UDP data

If your problem is that the data is too small, how about extending the data with random bytes? This will make the plaintext much harder to guess.

You have several choices. You can use DTLS, which is a version of TLS adapated for datagrams. It is specified in an RFC and implemented in the openssl library. You can also use the IKE/IPsec protocol and use a UDP encapsulation of the IPsec portion. Usually IPsec is available at the OS level. You can also use OpenVPN, which looks to be a hybrid of TLS for key exchange and a proprietary UDP-based packet encryption protocol.