The cards are great, I even use those outdoors around my orchids. Highly recommend them for flying insects.
Krissy, the question as to "how did all this happen" goes to where you bought your plants and how they were grown before you got them. If they were (most likely) greenhouse grown, they have been sprayed with all manner of insecticides already. Greenhouses are great breeding grounds for fungal infections and insect infestations and you can imagine commercial growers can't take the chance of letting anything spread through their huge greenhouse packed with plants.
The systemics like Bayer 3 - in - 1 are great up to a point then they fail. Since the stuff gets into the system of the plant, if it doesn't kill every single one of the insects on that plant, then the ones that survive will breed and their progeny will be resistant to the insecticide. Same as we've done to ourselves with antibiotics. If your plants were treated with that kind of stuff in the greenhouse before you got them, then what you have are a resistant strain of insects.
You've done exactly the right thing, spraying with soapy water. This is a "mechanical" insecticide in that it kills the bugs on contact. They can never develop resistance to it. Just be sure to do it again in 3 or 4 days to get the next generation because it kills the live bugs but not the ones still in eggs. After you get this big infestation cleared up, just take the plants to the sink or into your shower and spray them off with water at least once a week to keep the spider mites from coming back.
The fungus and gnats can be treated with a diluted solution of hydrogen peroxide. You can buy it at the drug store or grocery store, and then dilute it 1oz to 2 cups of water and douse the soil.