Wood – What type of glue should I use to repair the hardwood floor

I hate to be the one to tell you this, but there is really no magic putty or filler for shallow scratches and gouges in hardwood flooring. Even though there are a lot of colored wood fillers on the market, they are not designed for high traffic flooring or nuclear dogs. If it was just a couple of scratches you might be able to sneak by with a filler, but not for a refinishing job in a larger area as you describe. Most engineered flooring has 3/16" to 1/4" of hardwood veneer over a plywood base. If the scratches have not gone through the veneer, then you can sand the scratches smooth, stain to match, and refinish with 3 to 4 coats of urethane. I would recommend an oil based urethane. Apply 3 to 4 thin coats rather than 1 or 2 thick coats. Remember, the veneer is fairly thin and usually can only be sanded and refinished 2 or 3 times at best. Once the scratching penetrates the plywood base, your floor is unrepairable.

My advise would be to protect the floors with area rugs, runners, etc or keep the dog's nails cut short, or better yet, train them to behave in the house.

1. If as @gbronner mentioned its just the surface layer, that's pretty easy to fix: Scrape it clean, sand a bit, remove the dust, then apply poly. I wouldn't necessarily recommend this in the middle of a living room floor, but in a laundry room, I at least am less concerned about the appearance of the floor.

2. But if those boards are soft in the middle, they definitely need to be replaced and since they are being replaced you should also take a look at the sub floor to ensure there was no permanent damage to what is underneath. That said, If you have stopped the leakage you shouldn't have issues waiting for a contractor.

Please clarify the scenario we are working with here, surface damage or soft/rotted wood. If you are interested in fixing it yourself, I would suggest getting us a picture of the layout of the room (dimensions, and where the damage fits within those dimensions). We can suggest a best course from there.