Now the strange thing is, I added these addresses to omniwallet, and before I knew it, the contents of these addresses ( which was only 25% of my wallet ), and the contents of another address are transfered to a new address, and I lose everything.
It sounds like you were on a phishing site rather than the official Omniwallet site. It's also possible you have a keylogger that swept the private keys when you copied and pasted them.
In general, I don't trust web wallets. But even more than that, I would recommend against importing private keys (that hold BTC or valuable alts) to any website. Scams are too rampant these days.
1. Where did the mystery address 1JLE6ckXeLYcMQiGbCPDhsEFK56EiedGsw come from?
It looks to me like the hacker/phishing attacker imported your private keys into another wallet that included that address. He swept them all to another address.
2. What triggered everything going to the final location? - I've checked the BTC are still in that final address (1GDKbbYJawqfajQfLh3FLpKxP3xKWnfTrk ), so unlikely to be hacker .
For whatever reason, he wasted 0.00957563 BTC sending the output above to the same public address. It
is the hacker. He swept all the funds into one address and they haven't left that address.
Finally, how on earth do I get my coins back?
They are gone forever. Sorry for the loss. You need to be very, very careful about downloading malware or visiting phishing sites. Your computer may be compromised already; you should consider thoroughly checking it for malware or formatting it before putting any more funds at risk.
New users should really stick to hardware wallets like Ledger and Trezor until they learn more about the security risks of cryptocurrencies.
