You can find a YouTube playlist here with many of the songs suggested below.
Gathering
The psalm calls us to thanksgiving with our whole heart and this is picked up in Give thanks with a grateful heart (CH 180 / MP 170) and Praise, I will praise you, Lord / Je louerai l’Éternel (CH 175) while there are also more general songs of thanksgiving such as Now thank we all our God (CH 182 / MP 486), Give thanks to God (CCLI) by Scottish songwriters Allan McKinlay and Pete Crockett, or Praise and thanksgiving let everyone bring (CH 170), which would probably work best using just the first verse or two as a round. You could also use the more general call to sing praise to God at the end of v1 through Sing to the Lord a joyful song (CH 184), 10,000 reasons (Bless the Lord) (CCLI) or Come you thankful people come (Resound), with the latter having a simple call and response style which makes it very approachable for all ages.
Word
I shall praise you, O God, from my soul (CH 95) is an easy setting of Psalm 138 to pick up, almost imitating Spirituals with the repeated lines in each verse and the simple but soulful music. I give you praise, O Lord, with all my being (PCE / CCLI) would be an option for those looking for a familiar tune as it can be sung to Londonderry Air. With grateful heart my thanks I bring (PFAS 138A / Grace) is a fairly widely sung setting (although not one that I’m aware of being part of the repertoire in Scotland) which would appeal to those who enjoy Victorian hymnody as it is written by the same composer as “Jesus loves me, this I know”. Lord, I thank you (GIA) or On the day I called (OCP) are both good options for a responsorial setting with very attractive refrains.
Response
Who is my mother, who is my brother (MV 178 / Hope) picks up the questions Jesus asks in the Gospel and explores all the many people who Jesus calls family, including those who society often considers “other”. We can find similar ideas in songs such as In Christ there is no east or west (CH 624 / MP 329), We are one in the Father’s love (CCLI) and Jesus puts this song into our hearts (CH 692 / MP 376).
The focus on eternal life in the Epistle seems to link well with songs which focus on our trust in God through life’s challenges such as In heavenly love abiding (CH 551 / MP 331) and Yet not I but through Christ in me (CCLI), both of which hint at life beyond this on in their final verses, while Your grace is enough (MP 1178 / CCLI) has a similar theme without that explicit link. Fight the good fight (CH 517 / MP 143) looks more at the active choices we have to make to follow Christ in order that he “shall be your all in all eternally”.
If you are focusing on the Old Testament then there aren’t too many songs which link directly. It is God who holds the nations (CH 705) reminds us of God’s place in our nation’s life and also the freedom we are given to make choices. Lord, for the years (CH 159 / MP 428) prays both for our current society and the times we disown God, concluding with the need “to live for Christ alone”.
Sending
The broad theme of the Epistle is a natural conclusion with Love divine, all loves excelling (CH 519 / MP 449) and Ye that know the Lord is gracious (CH 642) some classic options focusing on eternal life. Who would true valour see (CH 535 / MP 224) is a song which divides opinions because of its language but picks up this theme while also linking into the Gospel. There is a higher throne (MP 1116 / CCLI) also links the two passages as we sing about “faithful ones from every tongue” who will find their place in heaven. You could also focus purely on this aspect of the Gospel reading with God is love: his the care (CH 193) or For everyone born, a place at the table (CH 685).