For straight cuts in thin plastic I cut right through or cut several times and snap.
Small internal corners: Drill holes and enlarge with a triangular file spun in my fingers like a reamer until I get the correct diameter and adjust them with a round file as sometimes they come out like rounded triangles.
Large internal corners, like Dougal, I use a compass cutter. after twenty five years of regular use, I managed to snap one of the bars of the inner section and will have to invest in a new one for larger curves
Square corners: I cut through in thin plastic and cut through partly and either chain drill to release the majority of the material before trimming with a scalpel and sanding, or drill a hole in the middle of the square, cut a cross and then use a razor saw to cut down the scores and snap the triangles out. The former technique reduces the chance of some material in the edge breaking away with the material you want to move and is best when using 2mm or thicker plastic.
Watch out for the type and age of the styrene you are using. If it is yellowing at the edges or on the surface it will be unreliable and may break where it wants despite your cuts etc. Some styrenes are more brittle than others and can be stored badly by the shop owner and thus will come out warped. The bluer styrene seems better than the creamier type but with care it is all pretty good unless perished.
For stepped or angled cuts, I draw a line along where I need to cut/file to to get my angle. You will probably get a slightly variable angle along the line so be careful and adjust where necessary. Remember, like wood, you can add slivers of plastic and when cured sand/trim back. Obviously we want to get it right first time, but it is forgiving. Steps I do by laminating thicknesses of styrene and reduce the dimension of the area to be stepped in one layer. So to step a 20mm square window down to 19mm, the inner layer has a square 1mm less in dimension. If making oddly shaped stepped areas, then mark and cut the larger dimensioned piece and then draw round it on a piece of styrene sheet and carefully reduce the line to get the inner dimension you need.
Styrene strip tips: Evergreen make good strips that have square corners, so can be used for accurate work, The ends are often useless, so cut the first 3-4mm off before making any accurate marks etc Also they can have tags of uncut material on the side at the end so watch out for that when using a set square.
They make good tubes but not good rod. The later is often not round and can have elongated voids like when stretching kit sprue.
Plastruct (not slaters plastikard) make reasonable strip but make excellent rod in a variety of diameters from .3 up to 6.3mm. It is matt and so easy to mark and is solid. Their tube is good as well.
Sllater's Plastikard is alright. Their rods are oval or of a brittle plastic and are not the best unless you are not after perfectly round rods.