As I explained via PM, there is no point in Bittrex giving you the private key unless Stratis and StartCoin use completely identical methods to derive pubkeys and address from private keys.
If their derivation methods are different in any way (ie. different network identifier/version byte(s) used, different hash functions used etc) then I would be willing to bet money that the private key they hold for the StartCoin address would generate a completely different Stratis address.
Essentially, what this boils down to, is that you've sent Stratis to a "random" Stratis address (that just happens to have the same base58 representation as some random Start Coin address that Bittrex apparently control)... whether or not anyone actually has the private keys to this Stratis address is currently unknown.
I hate to say it, but your chances of ever finding or generating the private key to this address are only a fraction of a tenth of not very much.