By saying not equal to any 1 of 3 possible values you mean equal to either of the other two possibilities.
so wouldn't that be:
=SUMIFS(Total ,Col 1, Crit 1, Col 2, Crit 2, Col 3, Crit 3, Col4, Crit 4) + Sumifs(Total, Col 5, Crit 5.1) + Sumifs(Total, Col 5, Crit 5.2) ?
Otherwise can you post your data and highlight what you require?
http://chandoo.org/forums/topic/posting-a-sample-workbook