Are there low-bit hashing or encryption functions for teaching cryptographical concepts?
Actually, lecturers/professors build simplified version of block ciphers and hash functions so that the students can understand better.
For Block ciphers there are;

Simplified DES by  Edward Schaefer in 96. You can also set it in Stinson's book Appendix G.
Simplified AES is first appeared on Cryptologia, 2003 by Musa, Schaefer, and Wedig.
Another Simplified AES Version again by Edward Schaefer
A Tutorial on Linear and Differential Cryptanalysis in 2002 by Hayes contains a simple SPN based block cipher to teach the Linear and Differential Cryptanalysis.

For hash functions;

Luhn Algorithm is a starting point.

A toy hash function  by Joshua Holden

In this paper I will discuss the requirements for a secure hash function and relate my attempts to come up with a “toy” system which both reasonably secure and also suitable for students to work with by hand in a classroom setting


Once  the Simplified version of AES is grasped, you can use them to build a hash function based on the Merkle–Damgård construction.

Also, this question Is there a simple hash function that one can compute without a computer? contains some others hash functions.