Aokiji is not intangible to the literal definition of the word but like other logia his body cannot be hurt or affected the normal ways. He enjoys the same advantage a sand or fire user does (thats what I mean with intangibility, dunno what a more proper word for it would be...). If we really get into the technicality though then hardly any of the logia we have seen would actually be intangible by nature. Magma, ice, snow, sand or swamp are pretty tangible as any liquid or powder would be (although aokiji is solid unless pierced). The issue here is that their form is not definite. Luffy is a perfect example of a paremecia for that matter. The issue with paramecia is that it is the widest category, it can incorporate anything that does not fit into the zoan or logia area.Luffy turns into a man made substance, elastic rubber. Diamonds are natural. Luffy is also a poor example of a paramecia.
We have seen all but one, in a limited number of panels.
Jozu has already been shown transformed. Diamond's are indisputably natural.
Intangibility is not a requirement for logia. Most logia users so far have logia elements that are intangible by nature. Aokiji does not become intangible when his ability his activated. His element exists in a solid state, the only solid logia element so far introduced. Other solid element logia will not grant intangibility either. They will probably act as armor, tangible but impenetrable without haki.
A natural element (occurring in nature), transformation into that element, and producing an infinite amount of their element. Jozu has already met the first two requirements. He arguably has fulfilled the third requirement as well, attacking the giants with giant "iceberg". An infinite stream does not mean he will have to shoot gemstones out of his hand. That would be kind of silly looking, anyway.
Why would it have to look like Crocodiles? Does a diamond ability have to produce streams of gemstones?
Well, a diamond logia would at a minimum have to have the ability to produce diamonds. In this particular regard it would make the most sense that a diamond ability would resemble sand the most. Otherwise his ability would physically resemble aokiji's but IMO that would be a tad weird. You'd see columns of diamonds all over the place... And still, we never saw an indication of jozu being able to make so much as a karat... If his ability is limited to turning his body to diamond but not generating any and actually damaging the diamond results in actual damage to jozu then there is simply no way that he can be considered a logia. Even if for a short while we did see him fight a bit. If he was a logia there would have been at least a slight clue. Then again an ability to generate at least a speck of diamond did not come up when blocking mihawk, or attacking crocodile or when doflamingo caught him with his strings or when he faced aokiji. We are talking about a logia user not generating a speck of diamond against a bunch of people whom he should have gone all out against.
that he's super strong or something ? But from what Zoro said he wanted to cut Diamond after steel & metal so won't real diamond be much stronger ? No Matter if Jozu has a Devil fruit ability or not he's clearly not invincible , chances are he has a devil fruit ability that let him cover his body with diamonds and underneath that he uses black Haki to make it even harder . Unlike character like Luffy you really don't have to battle cry everything you do . 