Breaking ICE - exactly how should strength be treated?
Unless otherwise stated, strength simply determines which icebreakers can interact with (typically meaning break subroutines on) a piece of ice. From page 16 of the rulebook:  


  An icebreaker can only interact with ice that
  has equal or lower strength than the icebreaker.


Notice that the individual icebreaker whose breaking ability you want to use needs to have high enough strength, the strength of your other icebreakers isn't a factor. It's also worth noting:


  Many icebreakers allow the Runner to temporarily increase the
  icebreaker’s strength by spending credits...This strength increase
  lasts only while the current piece of ice is being encountered, unless
  otherwise noted by card abilities. After an encounter with a piece of
  ice, the icebreaker’s strength returns to the value shown on its card.


Just to be clear, it's certainly possible that at some point in the future an ice will be designed for which the strength factors into some other effect (e.g. "do X meat damage. X is the strength of this ice"), but I don't believe there's anything like that in the card pool today.