Straight cut gears means that the gears themselves are cut at 90 degrees, ie the teeth aren't cut on an angle. Dodgy ASCII pic here:
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Angle cut gears are quieter and wear better too I believe, but won't cope with quite the same outright power as straight-cuts, particularly on very hard gearchanges (the whole gear face contacts at the same time).
A "dog box" refers to the gears having dog engagement, which generally means no synchros to wear out. Hardcore dog boxes are incredibly strong but without synchros you have to rev match, and unless you are flogging the car, they are a pain in the arse. Just to be pedantic, most manual gearboxes actually use dog engagement, but the synchros line the dog teeth up and make sure they're spinning at the same speed for a smooth gearchange. Calling something a "dog box" usually just means the synchros aren't there and that the dogs themselves are the only method of meshing the gears. FYI when you miss a gear and hear that horrible crunching sound, it's not the gear teeth grinding (they are in constant contact with each other), it's actually the dog teeth. If the synchros aren't doing their job or you've changed gears too quickly for them, the dogs will be spinning at different speeds and will grind.
Right, mechanics lesson over, time to go to work lol