I was thinking about this yester-day and realized that there are some characteristics of these phrases that also appear in the bass part during the choruses of "Brief Candles." Here are the first four measures (repeated as the next four measures):
(I'm still not certain what key the song is in, but I put the notation in A major. Also note that it's played an octave higher than notated)
In both parts, there's a steady five-pitch descent (B A G F# E in "Hung up on a Dream" and A G F# F E in "Brief Candles") occasionally punctuated by a note an octave higher (in roughly the same place in the rhythm), and this sequence is played twice in succession (just four measures in "Hung up on a Dream" but eight in "Brief Candles").
This is yet an-other musical element that lends some cohesion to the Odessey and Oracle songs.
(For what it's worth: I've previously written about musical similarities between "Brief Candles" and "Care of Cell 44" and between "Brief Candles" and "This Will Be Our Year.")