How can we reduce variables when converting from 3-SAT to 4-SAT?
The paper Effective Preprocessing in SAT through Variable and Clause Elimination covers the variable elimination techniques used in Minisat.  Broadly, variables can be eliminated by


Substitution, in which a variable to be removed is defined in terms of other variables in the formula and the definition is substituted everywhere in place of the variable.  Automatic Extraction of Functional Dependencies describes how to efficiently find (some of) these variable definitions.
Distribution, in which all clauses containing a negated literal of $x$ are resolved against all clauses containing a positive literal of $x$.  The produced resolvents are kept (minus any tautological clauses) and the original clauses containing $x$ are discarded.  The resulting formula is satisfiable iff the original formula was satisfiable.


The overall goal of the techniques described in the Minisat paper is to optimize the formula for exploration by a CDCL solver by reducing the total number of clauses and strengthening (decreasing the length of) the clauses that remain.
 You could of course (with exponential effort) eliminate all the variables, eliminating all the clauses as well if the formula was satifiable or leaving one or more empty clauses if formula was unsatisfiable.