I realise that it is frustrating, but hostility is just going to reduce your chances of getting assistance.
As long as your have the private keys, you can get the coins on all chains.
From the sounds of things, your BCH and BTG that match the BTC you had on Armory before your moved them have not moved.
Both BTH and BTG have relay protection, so if you sign on one chain it doesn't work for the other chains.
It doesn't really matter much, you just need a wallet of some kind for each.
BTG has not being doing very well on security, so if you tell a BTG client your keys, then you might lose your BTC too.
BTC is worth vastly more than BTG. You do not want to put your BTC at risk for the benefit of getting some BTG coins.
DO NOT DO ANY OF THIS UNTIL AT LEAST ONE OTHER PERSON HAS SAID IT IS SAFE
The first thing is to move your BTC to a new wallet so that it is protected by a whole new set of private keys.
Create a new "sweep" wallet on Armory for BTC. Move all your BTC into that wallet.
This means that your BTC balance will be zero for all other wallets. Therefore, you don't care if someone gets those private keys, since the accounts are empty.
You still shouldn't publish them obviously. Wait 6+ confirms before doing anything after that.
You can get a list of all private keys for a wallet by doubling clicking on the wallet
- Select Backup this wallet
- Select See other backup options
- Select Export Key Lists
- Click Export Key Lists
This gives you a list of the private keys for your wallet.
Make sure you don't export the keys for your new sweep wallet.
You can then import those keys into another wallet. It would depend on the wallet. I would suggest a web wallet since they are easy to setup and disposable. You can probably find web-wallets for BCH and BCG.
In Electrum, it is
Wallet -> private keys -> sweep
You then give a list. In your export file, you want to use the PrivBase58: option. It is possible that electrum will just read in your private keys. You might have to copy and paste the addresses that you want to transfer.