Before I get into the strategy of the deck, let's look at the most important card first: Fusion Parasite
This card can be used as a substitute for any 1 Fusion Material whose name is specifically listed on the Fusion Monster Card, but the other Fusion Material(s) must be correct. Cannot be used as Fusion Metarial otherwise. If this card is Special Summons (except during the Damage Step): You can Fusion Summon 1 Fusion Monster from your Extra Deck, using monsters you control as Fusion Materials including this card
This makes basically any Fusion Monster that needs a named monster along with otherwise generic requirements summonable with it as long as we can Special Summon our Parasite while controlling another monster that fulfills the other requirements.
How can we do that as often as possible: Reviving him by any means necessary. Good thing there's a lot of traps that can accomplish just that like Back to the Front, Call of the Haunted, Limit Reverse, Graceful Revival, Oasis of Dragon Souls, Powerful Rebirth and such along with Monster Reborn, Battlewasp Arbalest the Rapidfire, Kinka-Byo and Cross-Sheep.
However, many of those traps bring the problem with them that if the revived monster isn't destroyed they will stay on the field and clog up our backrow and how do we even intend to drop our Parasite into a position where we can revive him from in the first place?
The first problem is alleviated (but sadly not completely solved...) with Magic Planter thet gets rid of a Trap to give us 2 draws which might be new cards to revive our Parasite but he's still not in the Graveyard for said revive yet.
Here come multiple other cards into play:
We can easily Special Summon our Parasite from the deck with One for One and add him to our hand with Where arf Thou? (though that is more useful with Kinka-Byo) As for ways to dump the Parasite, we have Armageddon Knight, Dark Grepher (Reinforcement of the Army to search either of them), The Mathematician, Foolish Burial and Neos Fusion (Keeper of Dragon Magic to discard Parasite or anything else and search Neos Fusion).
So we now have enough ways to get our Parasite where we want it to be but what can we do with him now?
The two easiest Fusion Targets are Elemental Hero Brave Neos and Millennium-Eyes Restrict with Millennium-Eyes Restrict being our main play which is why we also run its support cards to efficiently cycle it.
Next we have the Fusions that require Warriors plus a named monster like Dark Cavalry (just becomes HUGE with all the backrow we're playing) and Red-Eyes Slash Dragon with Slash Dragon being one of the "ladderable" Fusions. We can Fusion Summon often and Slash Dragon being a Dragon enables us to use it for some more advanced plays. Never thought of hearing of a "Fusion Ladder" outside of a dedicated archetype like Lunalights, huh?
An honourable mention goes to Shura the Combat Star if we use Brave Neos to ladder into him since he can put on some pressure by making everything 0 ATK and floating into Idaten
Then we have the Fusions that require Spellcasters (like Millennium-Eyes Restrict) plus a named monster like Rune-Eyes Pendulum Dragon, another ladderable Dragon who's just big or the better Fusion target of this category being The Dark Magicians since they synergize REALLY well with this deck. Usually we're activating at least one backrow per turn so getting a draw out of it and if it's backrow being able to set and activate it is pretty insane. That basically equals another Fusion Summon per turn for basically no effort.
Now onto the Dragon Fusion monsters: We have Buster Blader, the Dragon Destroyer Swordsman easy to bring out with DNA Surgery if you draw it to lock down the opponent and allow huge damage. The alternative would be Dark Magician the Dragon Knight who protects our backrow since that's the most important part of the strategy.
Link Monsters include Linkuriboh because we run our fair share of lvl 1 monsters, Cross-Sheep because it gives us a revive on Fusion Summon turning a singular Parasite Summon into 2, Seraphim Papillon because I wanted a Link 3 that was generic and it can technically revive the Parasite and Linkmail Archfiend because having a lot of Fusions is great Fodder for his effect along with him being generic as well.
Since we run Link monsters we can also play Cyberse Clock Dragon. Not necessarily for the mill but for his ability to search any spall on death and him pulling attacks at himself as long as there's a Link monster on our field which is really easy to fulfill with all the lvl 1s we revive all the time and Linkuriboh