First of all, when you don't understand an assignment, then please ask your mentor! If the mentor doesn't answer then you probably missed some vital information. Ask around, if you cannot find anything, ask again. If still no answer is forthcoming, then escalate the issue to an advisor.
What you are likely asked to do is to implement a toy cipher. Such a toy cipher fully implements a cryptographic primitive such as TEA, however it will scale everything down to human proportions so it is easier to understand and - of course - debug. So there are tiny versions of AES and DES that can be used to learn about the algorithms and algorithm implementations.
For TEA there is Demitasse - a wordplay on tea (or coffee) served in a small cup, geddit? this is also called Simplified TEA by its original name. This cipher uses a word size of 4 bits internally, exactly what your assignment seems to require. Of course, this cipher is neither secure nor compatible with the full versions of TEA nor XTEA.
As for OFB, well, OFB is Output Feedback Mode, easily found on Wikipedia. The only question is which feedback size is required. By default I would make it easy for myself and implement full block output (nOFB, in other words, using the full 16 bit output of Demitasse / Simplified TEA), leaving 8 bit OFB as possible option if there is any time left. TEA itself is a block cipher, so if you configure it with OFB it turns itself into a full cipher providing confidentiality for binary messages with (almost) any size or contents.
In principle it is possible to perform OFB with an output size of 4 bits using the normal TEA algorithm. You just shift with 4 bits internally and output 4 bits as well. Of course, computers are very much byte-based, so this is slightly strange. Furthermore, you'd need one block encrypt per four bits which won't really help performance (however, with TEA and CPU's being pretty fast, it depends if this is an issue or not).