Regarding the if statements:
if all the animations they are executing are the same then you should be able to replace the ifs with just a single selector for the active slide shown at the bottom. That's kind of the point of adding a class like active so it's selectable.
tl.set($currentSlide,{autoAlpha: 0,className:'-=active'})
tl.set($nextSlide,{autoAlpha: 1,className:'+=active'});
tl.play();
if($nextSlide.index()==0&&$nextSlide.hasClass('about')){
var aboutH1 = $('.about h1');
slideAnim.to(aboutH1,0.5,{x:300},'-=0.5');
slideAnim.play();
}else if($nextSlide.index()==1&&$nextSlide.hasClass('team')){
var teamH1 = $('.team h1');
slideAnim.to(teamH1,0.5,{x:300},'-=0.5');
slideAnim.play();
}else if($nextSlide.index()==2&&$nextSlide.hasClass('case')){
var caseH1 = $('.case h1');
slideAnim.to(caseH1,0.5,{x:300},'-=0.5');
slideAnim.play();
}
// if all the above animations are the same then you should be able to replace the ifs with just a single selector for the active slide
slideAnim.to(".active h1",0.5,{x:300},'-=0.5');
slideAnim.play();