Stress can also generate lots of B.O. because it releases homones like adreneline into the body, and also makes one sweat more (even when they are not hot) Excessive B.O. may be a sign of other issues going on at school that she may be having trouble with. You did mention that the other kids were giving her trouble with these issues. It may be a visious cycle...other kids make fun of her, she gets stressed and breaks out in cold sweats, gets B.O, & the kids make fun of her BO, causing more stress....etc. You may want to look into some underlying stressful issues that may be affecting her and starting this.
If she's not showering, which may be the start of the issue to begin with, there may be something with the act of bathing and showering itself that she's trying to avoid. Is the water pressure too high? What about the shower head you have? She may like bathing versus showering, encourage her to try that. It could also be the pungent smells of the soaps, deodorants and other hygene stuff. I know I don't particularly like the strong smells of soaps and lotions. This issue may be as simple as buying unscented hygene supplies.
Shaving can be an issue with anybody. Rubbing blades and other things across one's skin can be particularly uncomfortable. If this is the source of the difficulty, like others have said, this is something that can probably be skipped, but I would recommend that your daughter wear clothing that would not expose areas that need to be shaven, and thus avoid the other kids ragging on her (and starting the B.O. cycle) For instance, she sould wear slacks, or opaque pantyhose that would cover her legs, and have her wear sleeved shirts that would not expose her unshaven armpits. Also, you could pick out some looser clothing for her. While this may not be that particularly in style for girls, clothing that "breathes" better will allow sweat to evaporate off her before it has a chance to build up and create undesireable odors.