Exegesis:
kai eporeuonto pantes apographesthai ‘and all went to have themselves registered’; kai connects the clause with v. 1 and this connexion makes of v. 2 a parenthesis (cf. Moffatt, Twentieth Century New Testament).
pantes ‘all people concerned,’ viewed in their totality; as compared with pantes the subsequent hekastos (in the singular), being a distributive pronoun, refers to the individual members of that totality.
apographesthai ‘in order to be registered,’ final infinitive, cf. on v. 1.
hekastos eis tēn heautou polin ‘each to his own town’; there is no need to translate ‘the town of his birth,’ because one could have a claim to landed property in a place other than one’s birthplace.
Translation:
Because of the parenthetical character of v. 2 it may be preferable to specify the transition and/or the subject, e.g. ‘therefore,’ ‘because of that decree/command,’ and/or, ‘all people (there),’ ‘all the inhabitants.’
Went, or, ‘set out’ (Zürcher Bibel), “made their way” (New English Bible), ‘rose to journey’ (Sranan Tongo), indicating the general upheaval, the next clause indicating the individual directions. Since the journey is to the people’s places of origin idiom may require ‘to go home’ (Balinese), ‘to go back’ (Bahasa Indonesia).
His own city, or, ‘his settlement of origin’ (Malay), ‘the settlement of his ancestors’ (Tae’; properly the term refers to the settlement of female ancestors, the traditional Toradja marriage being matrilocal), ‘his ancestral-house,’ lit. ‘his seat’ (Toraja-Sa’dan), ‘his clan-origin,’ lit. ‘the trunk of his nangka-tree’ (Batak Toba, the strong, but slow growing nangka, or Jack-fruit, tree being used metaphorically of the compound of a well-to-do family which remained in the same village for generations).
Quoted with permission from Reiling, J. and Swellengrebel, J.L. A Handbook on the Gospel of Luke. (UBS Handbook Series). New York: UBS, 1971. For this and other handbooks for translators see here . Make sure to also consult the Handbook on the Gospel of Mark for parallel or similar verses.