The phrase "almost any sort of" is correct and usable in written English.
It can be used when referring to a wide variety of types or categories of something, indicating that the statement applies to nearly all of them.
Example: "You can find almost any sort of cuisine in this city, from Italian to Thai."
Alternatives: "nearly any kind of" or "practically any type of".
An oval face can handle almost any sort of bang.
The chips can be almost any sort of wood scrap, including waste compressed into pellets.
The first is that he defends people's rights to enter into almost any sort of contract that they would like.
They turn out wrought iron work for buildings & almost any sort of metalwork you can think of.
Wondrously, Spore endows you with the power to create almost any sort of land-dwelling creature you fancy.
Eventually printed messages were added and today there are cards to suit almost any sort of sentiment from the sublime to the ridiculous.
Nor was there a wide audience for reports from a team of top psychiatrists about the devastating psychological impact on the men and their families of indefinite detention without trial, and of a house-arrest system framed by "control orders" that allow the government to place restrictions of almost any sort on the lives of those it designates.
You could apply it to almost anything, any sort of situation or structure that exists and may not always exist".
In another scenario, the air force tasks the drone — almost certainly, without any sort of weapons onboard — to do fly-overs of a G20 summit near Quebec City.
This is easily one of the most impressive committees of almost any sort ever put together at Princeton, much less by the trustees on any issue.
The e-mails reminded some precinct commanders of the blanket control the commissioner exerts — even the ceremonial unit of anthem singers and pallbearers reports directly to him — and of his thirst for arrests, of almost any sort.
