Styles, as played by internationally famous Rula Lenska, is a rarity in that she is a fairly major character who never meets The Doctor, or in fact isn't even told of his existence. For Styles and her hastily formed suicide squad, Resurrection of the Daleks is an entirely separate and different story to the one that The Doctor is experiencing, and that story really serves little purpose. From Episode One, Styles's sole function has been to break into the self destruct chamber and blow up the ship, Daleks and all.
Styles never gets to complete that mission - her and her compatriots are gunned down just as Styles is about to (rather casually, I thought) pull the lever to activate the self destruct mechanism. In essence, the entire subplot involving Styles finding the self destruct mechanism is to establish that there is a self destruct mechanism for Stein to finally use properly in Episode Four.
There's a lot of subplots that seem to go nowhere. The entire "Daleks create duplicates for every single character apart from Lytton" subplot is another one that seems to be needless. The whole dramatic reason for duplicates/doubles/androids is to have the original, good version of a character and his or her evil twin. There's never a scene that features both the original and duplicate character because after the duplicate is created, the original is killed. Couldn't the originals just have had their minds controlled by the Daleks, instead of going through the laborious task of creating duplicates? Also, if The Doctor has to go through the whole rigmarole of lying on a bed made of bubble wrap, have his mind connected to a tape recorder and be forced to remember all of his companions (except Leela) in order to have a duplicate made of him, then when do the other characters have this done?
Tegan is another character wasted in this story. She spends most of her time lying in bed, trading turns with Professor Laird to ask the soldiers when the ambulance will arrive. For Janet Fielding's last story, she sure isn't given a lot to do.