Exegesis:

en de tō poreuesthai autous ‘during their travelling,’ i.e. ‘when they were on their way.’ The use of poreuesthai (cf. 9.51-57 where it occurs five times) expresses that the journey to Jerusalem is continued. autous means Jesus and his disciples, probably not the small group of the twelve but a larger crowd.

eis kōmēn tina ‘into a certain village,’ without indication of name or place.

gunē de tis … hupedexato auton ‘a certain woman … received him.’ Nestle adds eis tēn oikian ‘into her house.’

hupodechomai (also 19.6) ‘to receive,’ ‘to welcome,’ always of receiving somebody as a guest into the house.

Translation:

As they went on their way, or, “as they continued their journey” (An American Translation).

If the shift from they to he (or, ‘Jesus’) and him is to be avoided (e.g. because it would suggest that, while the disciples did one thing, Jesus did something else), one may say, ‘as Jesus and (or, accompanied by) his disciples continued the(ir) journey he … him…,’ a rendering that is obligatory in some honorific languages.

And a woman … received, or better to link this clause to what precedes, ‘there a woman … received,’ ‘there lived a woman … who received’ (cf. Javanese). For the verb cf. on 9.5. Some languages require a specification by a locative phrase such as ‘in her house,’ which then is added not for textual but for linguistic reasons.

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.