As Jennifer has pointed out, you're not going to have enough time anywhere. I think you may be sort of kidding yourself by listing your itinerary the way you have, with each travel day attributed to both the place you're traveling from and the place you're traveling to. In actuality, that day will provide very little time in either place. This is the way I'd document your plan:
July 31: Fly into Edinburgh, train to Inverness (2 nights). Day-trip to Orkney (Aug 1).
Aug 2: Train/bus to Skye (2 nights). Just one full day to see Skye (Aug 3).
Aug 4: Train/bus to Oban (2 nights). Tour of the islands (Aug 5).
Aug 6: Train/bus to Glasgow (1 night). Just hours to see Scotland's largest city.
Aug 7: Train to Edinburgh (4? or 5? nights). Fringe Festival.
I like Glasgow, but you have to drop it. You need that day more in Skye. Personally, I'd drop that long slog of a trip to Orkney and go back sometime when you can spend more time there. But I am not very interested in prehistoric sites, which no doubt colors my advice.
Keep in mind that the weather in western Scotland is very changeable. Rain is common. Giving yourself only one day at prime destinations like Skye may mean you enjoy the scenery from the inside of a bus with rain sheeting down the windows. Even with multiple days it's a challenge to sightsee in western Scotland without a car, because tours, trains and even intercity buses often must be booked well in advance, before you can consult an even halfway-useful weather forecast.