Can you patent something that does not have a patent but is in use in non obvious way?
Nope. The underlying law for patentability (35 USC 102) says:
A person shall be entitled to a patent unless— (1) the claimed invention was patented, described in a printed publication, or in public use, on sale, or otherwise available to the public before the effective filing date of the claimed invention
So, if you are trying to patent something thats already known and used, you're out of luck. If you want to patent the practice of using something known for a new (and unknown) purpose, you can patent the method of using a previously known thing for that new purpose.
No, you cannot since inventions must be novel, unique beyond what is presently known.
Here in the UK, such a patent wouldn't be valid:
At IPO we do our best to ensure that the patents we grant are of the highest quality. It is possible that after grant some proof may be found that shows your invention was already known (called prior art). If this happens your patent will be invalid.
Intellectual property – guidance, Before you apply for a patent, IPO, 5 Feb 2015
I am not sure I got the question right. In particular: "in use in non obvious way". If you mean that a method or device is used maybe even publicly, but the product or device can not be understood or rebuilt by reverse engineering or at least the central part of the invention is **not publicly available or accessible ** (e. g. some machine where you can not see from outside how it works and it stays only in your / companys hands), then you can apply for a patent. But possible opponents and good patent examiners will for sure challenge this. So you may want to be sure already from the start what was availeble to the public and if the rest is obvious or not and therefore inventive. If I got it wrong and you clarify your question I could maybe give a better answer.