How can stains from stainless steel be removed

James, If really stubborn stains, you may have to use a chrome polish and buff. Check the attached links,instruction and guides, Good luck
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Cleaning Stainless Steel Appliances Cookware and More
Removing stains from stainless steel refrigerator
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You need to use ordinary soap as a lubricant and a fine steel wool to buff the steel surface. That will remove any built up surface debris completely but you may still have some discolouration of the metal remain.
An automotive polish designed for polishing stainless steel and aluminium (available from auto parts stores) might finish the job for you and remove much of any remaining staining but I would not use a chemical of that type on an inside surface that is used for cooking your food. (Same issue with those dreadful chemical and toxic oven cleaners).

Unfortunately, with use of the unit and heat , you will get some residual discolouration of the stainless steel.

Stainless steel does not stain, corrode, or rust as easily as ordinary steel (it stains less), but it is not stain-proof. There are different grades and surface finishes of stainless steel to suit the environment to which the material will be subjected in its lifetime. Stainless steel is 100% recyclable and is available in different forms, a stainless steel often used in knives pots and kitchen accessories.

stainless steel polish will do this don't get too abrasive a cleaner though,there are different coarsnesses of the product

Debruce Polish will remove these marks. DeBruce Polish is all you will ever need for your stainless steel and ceramic cook tops, polished granite, marble, porcelain, formica and glass. DeBruce is non-toxic odor-less and eco-friendly. You can get DeBruce on line at debrucepolish.com.

They also have a you tube demo "debruce method"

this stuff really works

use a stain remover like hapic, or gbc and the stain will go off.

USE OIL W/ VINEGAR OR GAS W/ THINNER THEN CLEAN IT

You say your new oven...and DW have stains...I will assume (if that's OK) that you have a stainless steel oven...and are washing stainless steel in the DW...but you are having streaks and or white...spots or deposits...Sounds like hard water...you may try a localized..(just for the DW and kitchen sink area) filtration system...to reduce hardness of water...(is this well water)..if so you definitely need filtration...if you don't already have it.
Here are some issues and or cleaning techniques for stainless steel.

stainless steel is known for its ability to be a clean surface that resists corrosion and rust. Dirt, dust and grime, however, put stainless steel at risk for corrosion and rust. Luckily, stainless steel responds well to cleaning, never wearing out from excessive cleaning, as long as certain rules are followed. 1. Water and a cloth.
Routine cleaning can be accomplished by using warm water and a cloth. This is the least risky option For cleaning stainless steel. Dry with a towel or cloth to prevent water spots. Wipe in the directions of the polish lines.
2. Mild detergent, (dish washing liquid) and cloth.
For cleaning that needs more power, mild detergent and warm water can do a great job without damaging the stainless steel. Make sure you rinse the surface thoroughly to prevent staining and spotting. Towel dry to prevent water spots which can be caused by minerals in water.
3. Glass cleaner for fingerprints.
Fingerprints are one of the biggest complaints about stainless steel, but can be taken care by using glass cleaner or household ammonia. Rinse thoroughly and towel dry. There are some newer types of finishes for stainless steel that resist fingerprints, a must if your pint-sized helpers leave their mark on your stainless steel appliances.
4. stainless steel Cleaner.
If you’ve had staining or scratching, or need to polish your stainless steel, a stainless steel cleaner may be a good option. Some of these cleaners and polishes can help minimize scratching and remove stains. They also can polish stainless steel surfaces nicely. Read the directions on the stainless steel cleaner and test in an inconspicuous spot. Be sure to rinse thoroughly and towel dry.

If this does not help please clarify...with specific model #'s and walk me through (step by step) what the specific problem is and how you address it....Thank you and I hope this helps.............
Good Luck...........The Fang.

We Use Debruce Polish in all our kitchens, especially cooktops and stainless steel. Debruce also works on polished granite, marble, porcelain, formica and glass. DeBruce is non-toxic odor-less and eco-friendly. You can get DeBruce on line at debrucepolish.com.

This stuff is perfect!