Your new oval, diamond sharpener is extremely coarse -- at least compared to a stone at the grit you should use for normal maintenance (i.e., sharpening before the knife is actually dull), and will eat your knives quickly.
I don't understand why 10 year old knives would become difficult to sharpen. Sharpened properly and as frequently as a professional environment requires, I'd expect them to be quite worn down. But difficult to sharpen, no.
Problem no. 1: Bluntly, problem number one is most likely poor sharpening technique.
Problem no. 2: The nature of a "medium" or "coarse" steel. Oval or round, the contact point with the knife is so small that the steel exerts tremendous pressure along the length of the edge. Consequently, any irregularities in your sharpening technique are are greatly magnified -- as compared to bench stones.
People don't realize that steels require a certain amount of skill to use -- gentle, regular pressure; limited number of strokes; etc. It's not complicated, but it does require going to the troulbe of learning. But even then -- steels are much better for truing than sharpening.
Problem No. 3: Again related to how steels work. Unless they're very aggressive, they don't so much sharpen (in terms of creating a narrow edge) as scuff up the old edge, and create micro-serrations. In the case of more aggressive steels, such as yours, those serrations aren't so micro. It turns the knife into a sort of saw with a coarse "set."
You get a knife which will "act sharp," rather than actually be sharp. Yes it will cut through a tomato; but it won't push cut well, and will tend to tear as it slices.
Not a Problem no. 1: For your environment, needs and skills -- this, and all of this, simply may not matter to you.
Just like choosing the "best knife" there are very few absolutes in sharpening. If you like it, it doesn't matter what "experts" say. Just keep doing it. What the heck, they're 10 year old knives anyway.
Vegetable oil: Under no circumstances should you use cooking oil on your sharpening equipment. It goes rancid, smells bad and clogs or glazes stones, and clogs a rod hone's (steel's) grooves. In fact, the whole point of using oil at all is to prevent your rod hone from clogging. Using cooking oil as sharpening oil is a very common, rookie kitchen mistake and has destroyed many communal kitchen whetstones. Because a steel isn't as porous -- it's not a big deal. Just wash your steel with soap, hot water and a brush. Something you should do on a regular basis, anyway.
Options: If you keep your steel clean, it won't need honing oil. If you don't keep your steel clean, it will need fresh honing oil every time you use it.
Soapy water works as well for sharpening as honing oil. For that matter, so does plain water. A clean, dry sharpener will cut quicker and more cleanly than a lubricated sharpener -- but will also need to be cleaned more frequently with soap, hot water and a brush.
I forget what passes for honing oil in Jolly Olde. Here in the states it's "mineral oil" which you can buy very inexpensively at any drug or hardware store. I understand it's sometimes avaialble under that name at UK chemist's but is quite dear. Another name for it is "petroleum oil," perhaps it's sold more cheaply under that name.
If you must use oil on your shaprening equipment, you can get by with unscented baby oil. Baby stuff tends to be sold at reasonable prices.
Good luck with your old knives,