Does your bleached hair get oily? (Not from products)

Hair shouldn't feel damaged and dry after bleaching. If it does it has been over-processed. All bleached hair has sustained some degree of damage though, and you may find that your more porous bleached hair soaks up the natural oil more than virgin hair did. The amount of oil your scalp produces can be affected directly after bleaching as the process is very drying to your scalp.

What do you use for shampoo + conditioner and how often do you wash it?

What do you use for shampoo + conditioner and how often do you wash it?

I use a sulfate free keratin shampoo (Renpure brand), but sometimes I also just wash with conditioner. I use the conditioner sparingly by the roots-very little by my top roots, mostly in the middles and ends.

My conditioner is Garner Fructis for dry and frizzy hair, and I also use either a Kerasys repairing deep conditioner or Organix Moroccan Argan Intense Moisturizing deep conditioning treatment. I generally use the Garnier and alternate with the Organix and the Kerasys.

I then wash and use a bit of coconut milk serum by Organix, heat protectant spray-Argan by Garnier Fructis,  and Organix Moroccan argan oil.

My roots are the same amount of grease as always. I have VERY greasy hair, maybe that's why it took the bleaching well?

I always used all this stuff EXCEPT for the second deep conditioners, before I bleached my hair.

It sounds like you have a good routine going 🙂 Have you tried doing vinegar rinses at all? Sometimes they can help people with oilyness

Luckily I have strong hair and despite being super processed it is not breaking off but it is really really dry even though I slather it in several conditioners and oils.

I also quit ironing my hair at all.

Will getting a keratin treatment restore the lost oils and add some moisture? I know my hair will be sleeker and straighter so the texture will improve if anything else.

No, often hair feels drier and more brittle after a protein treatment, which is why they should be followed with a hydrating treatment.
Bleached hair has a raised and rough cuticle, often parts of the cuticle are missing. Protein treatments fill in the gaps and smooth the raised cuticle back down, so the hair more closely resembles a healthy hair, where all the cuticle scales are tightly overlapped like roof tiles.
The damaged cuticle is less good at keeping natural moisture inside the hair, so bleached hair is also drier.
This is why bleached hair needs lots of TLC, the damage is permanent so you will need to keep adding protein and moisture.
Have you tried argan or coconut oils? These are better at actually penetrating the hair. Maybe try an overnight soak in oil after a protein treatment. The oils also help to prevent further protein loss.

I wonder what you mean by a keratin treatment, @xo123, because I am 😀 Queen of Brazilian Blowdry, hee hee.  I did have tremendous success in using it at home for the last few years, which of course incorporates the use of a straightener, and it allowed me to grow out my hair to a length I've never seen before in my life.

To be fair, I was not using any bleaches during those few years either, just brown box dyes mostly, so I really babied my hair quite a lot but will swear by the healing effects of keratin treatments.  I am continuing to use keratin blowdry every couple weeks on my now-bleached hair and still swear by the results.  I also agree with @WickedPixie that the tried-and-true "essential hair oils" are brilliant as well!  At the moment, I'm using a combination of all moisturising treatments and I think they all do something really good for my hair.