Is there an English word meaning "the use of uncommon words" or similar?
In the category of similar words, there's sesquipedalian, meaning prone to using long words.
Depending on how and why you want to use it, logorrhea (also spelled logorrhoea) might do the trick. It doesn't specifically mean using uncommon words but either a. excessive verbosity generally or b. a psychological disorder resulting in incoherent talkativeness.
As an added bonus it conjures up a little hint of a certain other word ending -rrhea.
1 a : designed for or understood by the specially initiated alone
a body of esoteric legal doctrine — B. N. Cardozo
b : requiring or exhibiting knowledge that is restricted to a small group
broadly : difficult to understand esoteric subjects
1. Understood only by a chosen few or an enlightened inner circle.
The writing in this manual is very esoteric; I need a degree in engineering just to understand it!
If you mean use of words or meanings that are outdated, you might be looking for archaic.
The prior answers appertain to the question more precisely, but I think in the right context, a word such as "ponderous," meaning laborious, dull, and excessively detailed, might be suitable; It also carries a more literary connotation than loquacious or garrulous, which describe speaking with superabundant wordiness, droning on, or talking in a roundabout manner.