I've found in various pieces LH harmony lines that don't seem to conform to simple I-IV-V or V7 function patterns. Or is there something deeper ?

1st example: Enya - Boadicea[/b] (mm-mmm... ;-)what a piece!)
Has C, G, G#, D# alternating in a not too predictable way. Picked up by looking at her hands in a YouTube video (and an amateur cover too), otherwise no way I could have...

If the key is G, the G# (aka Ab) may be functioning as the tritone substitution of the V chord (D) - The D# (aka Eb) would then be the V of the tritone substitute.

Just my $0.02 - I'm no theory wizard

You may be right, it may be in the key of Eb (or its relative, C minor). Didn't think to look at *flats* instead of sharps. Two flats are used, Eb and Ab. I hear no harmonic tritones (sounding in parallel). So C, G, G#=Ab and D#=Eb are VI-III-IV-I. It's supposed to sound Celtic anyway, and I don't know much in this area.

Piece #2: ABBA - Head over Heels[/b]
Don't have a pointer to its sheet music yet.
Most of ABBA is Mozart-like, I-IV-V but this piece sounds more 'chromatic' and unpredictable, based on a different sort of scale. Rhythm and sound like tango or another Latino thing...

Piece #3: ABBA - I Let the Music Speak
A score is at: http://pianomusicsheet.blogspot.com/
Also see the interpretation with Swedish mezzo-soprano Anne Sophie von Otter...

It does have several passages with a little chromatics and/or naturals beyond the written key - don't know if those are modulations, or a different mode, or just random chromatics to spice up a few spots...