Select a path / type etc and then apply a preset via the layer styles menu command or via the styles panel (found in the window menu).
Goto to the styles panel, if there is a bevel. Goto to the angle entry and rotate that to your desired angle. If the angle is 25 degrees and you want to change all the angles to 60 degrees more then set it 25 + 60 degrees. The reason for this, if you go to the gradient then the gradient maybe set to 100 degrees so you will want to add 60 to that (if you want to keep it consistent but you don't have to rotate the angles to the same at all, there is no requirement for that, all that matters is that the it looks as you want it)
If there is a gradient, go to that and select the angle for that though if there is a gradient and you are using radial then changing the angle of rotation will make no difference though it will if the gradient is set to linear or reflected say. You can now add multiple gradient overlays to your layer.
If the style has a pattern overlay, you can now go to the angle for that also and change that by the additional amount (say 60 degrees).
To finish off, if there is a shadow, go to the drop shadow and change that if there is a drop shadow and do the same with the angle there.
If you don't want to do this, you can also apply a destructive rotate effect by going to the layer menu and layer styles and create layers command and that breaks it apart into separate layers with each of the effects such as the drop shadow as well as the bevel etc and they are all separate and cannot be modified now as effect. If you go to the layers panel you will now see all the individual layers which you can select and then apply a standard rotation by using the bounding box (if you have set the show bounding box on along the top options bar). Rotate the pattern overlay layer, rotate the drop shadow layer and so on. This is a destructive effect.
Once you have created all your individual layers, select all those layers in the layers panel (below the type layer, do not add the type layer into the smart object) and then go to the layer menu and smart objects and convert to smart object. You can now select the smart object and rotate the smart object and you will see the patterns and bevels and gradients etc all rotate and you can always change the panel as well as apply additional effects / filters etc.