Pogue Mahone's sessions are on Wednesday nights unfortunately - but are well worth catching as some very accomplished musicians sometimes drop in.
I don't think there is much going on at Flanagan's Apple these days but there could be an occasional casual session. I think the same sort of arrangement applies at Scruffy Murphy's i.e. something sometimes happens but without anything as organised as prior planning involved. If you turn up with a fiddle maybe someone else will encourage you to play it, or they may just chuck a penny in your cap and send you packing!
Just for the record here is a fairly current list of Irish music sessions in the North West Irish Sessions in UK North West