τοῖσδεσι: a version of τοῖσδε that appears in Homer but also in later Greek authors such as Democritus, Hippocrates, and Plutarch (accented in Homer and Hippocrates and occasionally elsewhere as τοίσδεσι). πρός +dat. commonly means "in addition to" or "besides" (LSJ B.III).
εἰρημένοισι: Perf. pass. participle dat. pl. from λέγω, "spoken, promised." -οισι(ν) is Ionic for -οις (S. 230d).
σεωυτὸν: Ionic for σεαυτοῦ -ῆς, (also contracted in Attic to σαυτοῦ, -ῆς), 2nd person reflexive Pron. "yourself" (only appearing in gen., dat. and acc. sg., masc. and fem.).
ὁρεόμενον: ὁρέω is Ionic for ὁράω. The middle voice is used by poets like the active.
εἴσεαι: Ionic 2nd person singular future indicative from οἶδα (= Att. εἴσῃ).
καὶ σεωυτὸν ἕνα δοκέοντα ἄλλον ὁρεόμενον καὶ ἄλλον ἐόντα εἴσεαι: "You will know that, though you seem (to be) one, (there is) one 'you' that is visible and another which you are.” With verbs of knowing, showing, and perception, indirect statement is expressed with a subject accus. and an accus. participle (S. 2106 and 2110).
οὔνομα, -ατος, τό: Ionic for ὄνομα.
ἐφαντάζεο: “you used to appear.” This form is Ionic 2nd person singular deponent imperfect (from φαντάζομαι).
χρόνῳ: "in time"; the dative can be used to indicate the span of time within which something may happen: S. 1542c. In this way, the genitive and dative can express similar ideas about time (S. 1447a and S. 1543). In prose, it is rare for this dative to appear by itself (as it is usually introduced by ἐν or at least has an accompanying adjective).
μεταβήσεαι: Ionic 2nd person future middle from μεταβαίνω.
ἐς ἄλλον: "into another (person)." As is clear from the ending, this is a masculine substantive referring to the next person into which one transforms (neuter acc. would be ἄλλο).
τάδε μὲν ἱκανῶς: "these things (sc. have been discussed) sufficiently"
τὰ δ᾽ ἀμφὶ δίαιταν ὁποῖός τις εἶ: "What sort of person are you with regard to things having to do with diet.” The term δίαιτα covers more than just diet, and includes lifestyle, physical regimen, and so forth. But as becomes clear, this discussion is about food. τὰ δ’ ἀμφὶ δίαιταν is an acc. of respect (S. 1601b) with the definite article turning the prepositional phrase into a substantive (for the substantival power of the definite article see S. 1153).