A.T. Robertson Commentary Acts 16:17

"The same following after Paul and us cried out, saying, These men are servants of the Most High God, who proclaim unto you the way of salvation." — Acts 16:17 (ASV)

The Most High God (του θεου του υψιστου). Pagan inscriptions use this language for the Supreme Being. It looks like supernatural testimony like that borne by the demoniacs to Jesus as "son of the Most High God" (Luke 8:28. Cf; 3:11; Matthew 8:29; Luke 4:41, etc.). She may have heard Paul preach about Jesus as the way of salvation.

The way of salvation (οδον σωτηριας). A way of salvation, strictly speaking (no article). There were many "ways of salvation" offered to men then as now.