"Stilted language" means language that is self-conscious, awkward, old-fashioned, overly formal, or unnatural.
"Stilted" with that meaning only applies to language.
Stilted language: "My dear sir, allow me to express my great pleasure at having made your acquaintance and beg to hope that we may make an engagement for luncheon the next time your peregrinations bring you to this vicinity."
Natural language: "I'm pleased to meet you and I hope we can get together for lunch the next time you're in town."