Starting on August 1st, will ALL transactions in the blockchain be in segwit format? Is it a format imposed if you want your transaction included in the blockchain? Or is it optional?
Segwit is completely optional. If you don't want to use it, you don't have to and you can use Bitcoin as you normally do now. It is completely backwards compatible so you can use non-segwit software even after segwit activates. The current transaction format, script types, and addresses aren't going anywhere. They will remain the same and unchanged and will function as they do now.
Also, segwit is not activating on August 1st. Segwit will be activating some time around August 24th as that is around when the lock in period will end. First it has to become locked in though. Over the next 2016 blocks, 1915 of them must signal for segwit in order for it to become locked in.
Or there is no transaction format change at all and it is just about the way it will be stored in the blockchain by the miners?
There is a format change, but only if you are spending from segwit outputs.