What is the best-known inapproximability result for MIN-3CNF-DELETION?
There is no approximation algorithm for MIN-3CNF-DELETION at all since it is not even possible to determine in polynomial time whether a 3 CNF SAT instance is satisfiable or not (if P≠NP). That is, it is not possible to determine if the objective function is equal to 0 or strictly positive. Specifically, if we had an $f(n)$ approximation algorithm for the problem, given a satisfiable instance the algorithm would find a solution of cost $0 \cdot f(n) = 0$ ; that is, a solution that satisfies the instance. 

In contrast, if an instance of Min-Horn-Deletion or Min-2CNF-Deletion is (completely) satisfiable, we can efficiently find a solution that satisfies all clauses. Thus it makes sense to talk about approximation algorithms for Min-Horn-Deletion and Min-2CNF-Deletion.