Just an attempt to see if I am up to date -- using English a a compromise among the several formal systems and ignoring phonological details that tend to divert the discussion and confuse the reader.
Word classes, each phonologically distinct, though their forms are not decided.
predicates (each of fixed adicity, though this important feature is not, apparently, to be marked)
names (any phonemic string enclosed in audible
quotes. these are ranked with predicates and are either monadic -- in which case no naming operator is needed -- or medadic -- in which case, they enter formula only as complements to the naming operator)
variables
unary propositional operators (negation, affirmation, tenses, modes, ...)
predicate makers (agentive, event, specificity, naming, proposition, ...)
binary propositional operators (AND, IOR, simultaneity, ....)
quantifiers (ALL, SOME, CERTAIN, ...)
speech act indicators
interjections
A formula is: an n-adic predicate followed by n variables (separated by an audible separator)
a unary propositional function followed by a formula (variables remain bond or free as before)
a predicate maker followed by a variable followed by a formula (in the case of naming, followed by a name) (variable remains bound or free as before)
a binary propositional connective followed by two formulas (binding and freedom remain unchanged)
a quantifier followed by a variable followed by two formulas (free occurrences of the indicated variable in the complements are now bound by this quantifier, as is the indicated variable, otherwise bondage and freedom are unchanged. Well, the situation of bound occurrences of the indicated variable in the complements is up for discussion)
a speech act indicator followed by a formula (binding and freedom unchanged) this is also called a sentence.
any of the above with interjections before, between or after
mentioned components (not between predicate makers or quantifiers and their variables).
I haven't touched on termsets because a) I am not through absorbing the going model and comparing it with my sketches and 2) I think any static description is bound to be inadequate and/or misleading, while only logic to language transformations will cover the possibilities (the lack of these in Lojban is yet another reason why the Lojban to logic translations are so non-trivial, if not non-existent).