How to clean dishes without a dishwasher

We don’t have a dishwasher right now. We are renovating the kitchen.

My husband sometimes washes the dishes and he thinks a sponge is just fine but I know how dirty and gross sponges are and the dishes are basically not even clean.

Our dishes sit out for days because I’m so sick with morning sickness right now I can’t stand the smell of doing them.

I usually soak them all in soap again after I wash them in dish soap and sponge. Basically washing them for a second time completely.

My husband thinks this is pointless. He thinks the sponge is enough and it’s SO GROSS!!!!

The dishes are so nasty after he washes them. They still feel greasy and gross. I don’t understand his mind when it comes to this.

When I soak them all in soap for a second time and use my clean hand they feel clean. The sponge just moves shit around.

I hate this system it sucks.

Can I soak them in vinegar or something to get them cleaner?

Edit: We use new sponges frequently but I still find them gross after only using them on a few dishes. What I mean by spread around is that all the dirty stuff is off the dish visibly but it still feels dirty so to me it seems like it’s just moving the bacteria and such all around not really cleaning it. We use dawn. Idk how they still come out greasy after he washes them I think he’s just bad at dishes?

The main issue is that the dishes sit for days and pile up and it drives me insane. I think it’s so nasty but I can’t bring myself to do them cause I’ll barf and my my husband sucks at washing them so I feel like I’m the only one that’s gotta do it. I’m so close to throwing all my dishes away and buying plastic cups and plates.