Dry Hair Guy Needs Guidance For Style Goal

You should be washing it as much as you need to wash it to get it as clean/dirty as you want it (this varies for everyone).  Go for shampoo only, then follow with a conditioner instead of doing the combo shampoo and conditioner.  Conditioner alone at the end will help with the dryness problem. 

You should also definitely try diluting your shampoo, this will help with both dryness and oilyness.  Shampoo is very concentrated, and you can dilute it quite a bit with water and still get suds.  Diluting will help keep it from overdrying your hair, and will help your scalp get less oily because your scalp will overcompensate less for the dryness.  I know you said you like it when it gets oily, but getting it so you have to wash it one day less frequently (which diluting the shampoo will do) will help with the dryness, I'll talk about oil in a minute.  Get a small bottle and use it to dilute your shampoo - you can mix it half and half with water, then see how much water you can get away with adding to still get suds when you wash (you can probably go at least 3/4 water).  Roll it to mix it, don't shake it, and use a small bottle so you only have to mix what you need per day (its best not to let it sit around in its diluted form).  It will take a few weeks to 2 months for your scalp to adjust, but after that you can probably go that extra day without washing.

Now, oil.  You like it oily because it makes it more limp / hang straighter like in that photo.  His hair is pretty straight, so you may need to straighten with an iron to get it like that, but that heat will be VERY drying, so you may not like it.  You can try putting a drop of oil in it if that gets it to hang the way you like, and that will be much better for your hair, and also help with its dryness.  You can use jojoba oil, coconut, or even try olive oil from the grocery to see how you like it.  Use only a drop and spread it through your hair.  It won't look oily unless you use too much - if that happens, just use less.  At your length, one drop of oil will probably be plenty. 

Another problem that may be leading to your dry hair problem is silicone buildup.  I don't know what products you've been using, but getting a clarifying shampoo and using it once would greatly help if that is part of the problem.  Any shampoo that says "clarifying" on it is what you're looking for, but this is only for use once every 2 months or so, it is a very drying shampoo, it WILL make your hair feel like straw, and should only be used for buildup removal on the very rare occasion.  Use a heavy conditioner afterwards to add back the moisture you will lose from it.