They have sharpened their tongues like a serpent - Compare the notes at Psalms 64:3. The idea here is, that since the tongue of the serpent “seems” to be sharp, pointed, adapted to penetrate (and probably the original reference in the image was derived from that idea), the wound inflicted is by the serpent’s tongue - “as if” with a hard, penetrating point. It is now known, however, that it is by a tooth - a single tooth, made flexible for the purpose - at the root of which a small bag containing the poison is located, which is injected through an orifice in the tooth into the wound. The meaning here is, that the words spoken by such persons - by their tongues - were like the poison produced by the bite of a serpent.
Adders’ poison is under their lips - The asp or adder is among the most poisonous of serpents. Thus, Cleopatra of Egypt is said to have destroyed her own life by an asp, which she had concealed for that purpose. This passage is quoted in Romans 3:13, as a proof of human depravity. See the notes at that verse.