re: octave strings on normal fiddles - yes this is essentially putting much heavier strings on which play a whole octave below the normal pitch of a fiddle. It can work... and it can not work. Depends a lot on the natural resonance of the instrument itself - I've heard octave violins that sound thin, fuzzy, and quiet, which as far as I know is all down to the size of the airspace that is vibrating (that being the reason why cello bodies are as large as they are). You can get purpose built octave fiddles which have the same scale length as a normal fiddle but have deeper bodies and thicker ribs. A fairly modern invention, and again, some work better than others imho.

re: fiddle accompaniment of songs in general, something I have done a bit of myself with or without other instruments... at any one time I tend to choose either to be doing something rhythmic and chordal, to add texture and fullness of sound, or doing something harmonic which is almost treating the fiddle as a second voice. Either way the primary focus HAS to be supporting the song and whatever I try to add by way of drama, texture, and fullness of sound needs to not dominate or take over. Often difficult to tell from the inside whether this is working or not and recording of practices is a very useful tool. As rules of thumb I'd say when starting out, less is more. But too little can be dull and pointless... it's often just a question of keeping experimenting. Another tip - analyse what other accompaniments that you like are doing - no matter what instrument they are on. Think about what the accompaniment is adding - and how it is doing it. Then see if you can produce a similar effect on the fiddle.

Michaelr - you're saying that you don't think the fiddle 'does rhythm too well'? I'd be tempted to say 'lots of fiddle players don't do rhythm too well' instead. The fiddle is an extremely flexible instrument and can be played in a very rhythmic way. It's just that lots of players either don't try to or aren't too good at it.

Lastly, I'd definitely second all of JohnB's suggestions (Barry Dransfield, Nancy Kerr, Eliza Carthy and John Boden). I am constantly blown away by what Nancy does with her fiddle as an accompanying instrument - even more impressive in that she's often accompanying her own singing. Not sure if there is any footage on youtube but if you can find a video of her doing 'Dance to your Daddy' you'll probably see what I mean.