You seem to be a bit confused regarding wallet names 
1) For BTC, you want Electrum... I'd recommend v3.0.3... available here: https://electrum.org/#download
2) For BCH, you want ElectronCash... I'd recommend v3.1... available here: https://electroncash.org/#download
3) For BTG, the only real wallet I can recommend is BitcoinGold Core... available here: https://bitcoingold.org/downloads/ (NOTE: requires FULL blockchain download)
There is no "lightweight" wallet that I know of for BTG that I would consider "trust worthy"... there certainly isn't an "Electrum" fork like ElectronCash etc.. There is the option of using Coinomi (requires Android, although, theoretically, you could install the BlueStacks Android Emulator on Windows and use Coinomi there).
For 1) and 2)... I *HIGHLY* recommend that you check the digital signatures for the downloaded wallet installers BEFORE running/using them... there are a LOT of fake websites that look IDENTICAL to Electrum and ElectronCash websites and it is VERY easy to download a fake wallet that will steal your coins.
As for the actual process, it would be fairly easy... simply import your MultiBit HD seed into Electrum, move your BTC to a new wallet... then import your MultiBit HD seed into Electron Cash... move the BCH to a new BCH wallet... finally, you would need to either import your seed into Coinomi to get BTG... or use https://iancoleman.io/bip39/ along with MultiBitHD seed to get the private keys to import into BTG Core.
1) For BTC, you want Electrum... I'd recommend v3.0.3... available here: https://electrum.org/#download
2) For BCH, you want ElectronCash... I'd recommend v3.1... available here: https://electroncash.org/#download
3) For BTG, the only real wallet I can recommend is BitcoinGold Core... available here: https://bitcoingold.org/downloads/ (NOTE: requires FULL blockchain download)
There is no "lightweight" wallet that I know of for BTG that I would consider "trust worthy"... there certainly isn't an "Electrum" fork like ElectronCash etc.. There is the option of using Coinomi (requires Android, although, theoretically, you could install the BlueStacks Android Emulator on Windows and use Coinomi there).
For 1) and 2)... I *HIGHLY* recommend that you check the digital signatures for the downloaded wallet installers BEFORE running/using them... there are a LOT of fake websites that look IDENTICAL to Electrum and ElectronCash websites and it is VERY easy to download a fake wallet that will steal your coins.
As for the actual process, it would be fairly easy... simply import your MultiBit HD seed into Electrum, move your BTC to a new wallet... then import your MultiBit HD seed into Electron Cash... move the BCH to a new BCH wallet... finally, you would need to either import your seed into Coinomi to get BTG... or use https://iancoleman.io/bip39/ along with MultiBitHD seed to get the private keys to import into BTG Core.