They look Teak to me and it's veneer, the only solid wood is the bull nose @ the 90 degree turns. I'm a furniture finisher by trade and you look like you pretty handy so I can guid you to do a easy and very nice finish.
You might want to buy a spray mask, and a box of latex gloves that can handle being in lacquer thinner.
The cabinets now have teak oil on them, you can wash it off fairly easy with lacquer thinner and lots of rags. Two gal. of thinner will be plenty, and you''ll want to do it outside for fresh air. I say lots of rags and thinner because your washing off the oil and as the rags get dirty you get new ones. When the rags don't get very dirty anymore, you have successfully washed 98% of the oil out of the wood and your done with the stripping.
The next step is to steam the wood....this will pull a bit more oil out but the main thing is to lift the dents and most the scratches. Clean rags, a bucket of water and a household iron is what you need. Taking a side at a time, wipe water on it with the rag, lay the wet rag flat on the wood and iron...lots of steam, do the entire surface of the outside of the cabinets. This swells the pours of the wood and soft dent will pop back up as it dries to the level of the rest of the veneer. It's only going to do so much though, don't over steam and expect it to lift very bad damage. As your rags and water get dirty doing this change them, as with the thinner and rages, keep getting rid of the dirty so your not just spreading it around.
Now one thing I would not!! do is sand them with a machine. People who don't finish or just have in their mind that they are going to do a supper sanding and make them perfect really only loose all character that took years to get. Just hand sand them with 180 grit, with the grain no need to over do it, they will get smooth enough.
We can talk about the rest of the step when you get to this point...
