οἶσθα is from οἰδ θα; ἴστε from ἰδ τε; ἴσθι from ἰδ θι ( cross83). ἴσμεν (older ἴδμεν) gets its ς from ἴστε ( cross87). ἴσα_σι is from ἰδ σαντι, with ς from (Hom.) ἴσαν ἰδ-σαν with the ending -σαν (cp. εἴξα_σι 704 d). ᾔδη is for ἠ-είδη with η as augment ( cross433).
Herbert Weir Smyth [n.d.], A Greek Grammar for Colleges; Machine readable text [info] [word count] [Smyth].