Exegesis:

ēn de ekei agelē … boskomenē ‘now there was a herd … feeding.’ The clause describes circumstances that are relevant to the event that follows. ēn … boskomenē is periphrasis of the imperfect and serves to stress the durative aspect.

boskō here passive ‘to graze,’ ‘to take food,’ in v. 34 active ‘to give food,’ ‘to tend.’

agelē choirōn hikanōn ‘a herd of many pigs,’ or, with a shift in the syntactic pattern ‘a large herd of pigs.’

agelē (also v. 33) ‘herd.’

choiros (also 15.15ff) ‘pig,’ ‘swine.’

en tō orei ‘on the hillside’ or ‘on the hills.’ The article does not refer to a specific hill, or mountain, but is used in the same loose way as in the English rendering.

kai parekalesan auton hina epitrepsē autois eis ekeinous eiselthein ‘and they besought him that he would permit them to go into them.’ For parekalesan (aorist, implying that the request would be granted) cf. on v. 31.

epitrepō ‘to permit,’ ‘to allow.’

Translation:

Was feeding, or, ‘was seeking (something) to eat’ (Bahasa Indonesia); or, introducing an indefinite personal agent, ‘they brought … swine there, to go seek food’ (Sranan Tongo). The verb used in Ekari lit. means ‘rooting,’ i.e. seeking tiny sweet potatoes in a fallow garden.

On the hillside, or, ‘on/along the hill.’ For ‘hill’ cf. on 3.5.

They, i.e., the demons, may have to be specified.

Begged him to let them enter, or, ‘asked him, “Please, allow us to enter” .’ For the latter verb see v. 30, but since the demons use it here with reference to themselves, the rendering to be used should not have a decidedly pejorative connotation; hence differentiation may be necessary, e.g. in Bahasa Indonesia (RC and 1968), Balinese, Sranan Tongo.

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.