I worked on a Traulsen two door, upright refrigerator today. It had a Sporlan BIJ 1\8 tev on it without a reciever.
Most small capacity self contained refrigeration systems that do not employ head pressure control can generally get by without a receiver.

I needed to replace the valve, my supplier is unfamiliar with this valve, as am I.
The Sporlan BI series TEV is an OEM style valve, normally supplied non-adjustable.

The refrigerator has a 1/3 h.p. compressor. I replaced the valve with a EFF 1/4 C. Am I correct in assuming the 1/8 on the original TEV is for 1/8 ton?
Yes.

If so am I oversized?
Perhaps a bit. But the EFF-1/4-C is an adjustable valve, and one could expect it to control reasonably well on an application such as this with the proper setting. Getting the proper setting on a TEV that is oversized somewhat, however, will be more tedious than with a valve properly matched to the system's design capacity.

The Prof would have used an EFF-1/4-C in this situation, assuming the wholesaler did not have an EFF-1/8-C in stock.

I am experiencing some hunting, about 9 degrees of superheat.
What are your high and low values of superheat? What is the approx time it takes for the superheat to go from its low value to its maximum value and back to its low value? Is the evaporator coil top or bottom feed?