The Remainder of Jesus' pre-Jerusalem ministry

(Mark 3-10 -- this section rightfully includes Mark 2:13-22 but I have included this section on the call of Levi and subsequent debates with the call of the first four disciples above.)

Much of this section is covered by MacDonald's observations. I have added only two sections here, although both are related to the same narrative episode in Mark.

What to take on a journey
The parallels here may measure up on the distinctive and explanatory criteria (e.g. why the disciples were not to carry a bag) but two points in the gospel do not follow the same sequence as their "would-be match" in the Homeric epic. Make of these similarities what you will.

When Jesus in Mark's gospel sends out his disciples in pairs (two by two) he told them to take nothing except a staff with them. He specifically tells them to take only one, not two, cloaks. No bag or money was allowed either, but they could wear sandals. Once in a town they were to stay only at the one place that gave them hospitality, presumably as opposed to wandering between different houses in the one place.

Was Mark thinking of the journey of the twosome Odysseus and Eumaeus, beggar and swineherd, to the town where Odysseus planned to cast out the suitors and reclaim his kingdom? Odysseus asked for a staff since, he said, he had heard the way was rough. He has only one cloak, because when he first met Eumaeus much was said by Eumaeus that he had only one to offer, not two. Eumaeus is also depicted binding his sandals before setting out on the journey. If Mark did have these two characters in his mind then he has emulated Odysseus by having Jesus' disciples going one better than the Homeric hero: like Odysseus they are not allowed two cloaks, but are allowed a staff and sandals; but unlike Odysseus they are not to carry a bag.

The background setting to the two journeys is also distinctively similar -- both have just returned to their own home countries or towns, but are despised and rejected there. Jesus is not recognized for who he really is, and Odysseus must disguise himself as a beggar.

Jesus' disciples
Odysseus & Eumaeus
After rejection by home town -- unable to do mighty works -- he is despised as a nobody by his own people Odysseus must disguise himself as a despised beggar because of those who reject him in his home of Ithaca -- Melanthius abuses him
then sends disciples to travel in two's then travels as a pair, with Eumaeus
to towns to town
to cast out demons to cast out suitors
and preach repentance and reclaim kingdom
to stay in the one house not to go around town but stay put in one house (Eumaeus was also instructed in an earlier trip to town to be sure to go only to the one house)
Take a staff Carried a staff
But no bag or money And a beggar's bag
Not to take 2 cloaks Eumaeus did not have a second cloak to give Odysseus (This and the following detail are from an earlier scene than between Odysseus and Eumaeus)
And sandals Eumaeus bound his sandals before setting off

On returning from a journey to ghosts and demons

Jesus' disciples (Mark 6:7-32)
Odysseus and crew (Bks 11, 12)
Jesus sent his disciples on journey to cast out demons (Mark will use the disciples of Jesus to transvalue Odysseus) Circe sent Odysseus and his crew on journey to place of the dead
and given power over unclean spirits to have power over departed spirits
cast out many demons and healed many (Jesus' disciples transvalue Odysseus -- even they are greater than Odysseus!) Odysseus could not save or heal any
flashback to death of John the Baptist -- many think he is one of the dead prophets returned Odysseus meets Agamemnon (see above on John-Agamemnon correspondences) and learns how he had died -- meets another departed prophet and heroes, too. Also hears how Elpenor died.
when disciples of John hear of John's death they came and took away his corpse and buried it when crew of Odysseus hear of Elpenor's death they returned and took his corpse and buried it
Jesus' apostles return to Jesus Odysseus and companions return to Circe
        and tell Jesus of all they had done  
        Jesus took them aside away from the many others (Mark's reference to 'there were many coming and going' is very vague and odd -- was he trying to fill in the gap left by his model having Odysseus being taken aside from the crew? Did Mark thus have to suddenly invent a crowd to justify the taking the disciples aside? -- Criteria 6)  
they did not even have time to eat ... (Another transvaluing of Odysseus and his companions by Jesus' disciples) Circe gave them plenty of food and rest time to eat after their return ...
          Circe took Odysseus aside away from the others
          and Odysseus told her all they had done
... so they went to isolated place by boat ... before they continued their journey by boat