I have just taken up a new job at a different region from where I now live with my family. The job comes with an unfurnished accommodation. I am not currently financially OK to furnish the house. Is it OK to ask the company for a financial help to furnish the accommodation and how do I approach the issue?
You're free to ask for anything you want, but it's unlikely that you're going to get the response you're hoping for. The time to negotiate things like relocation assistance or a signing bonus (which is essentially what you're asking for) is before you accept the offer, not afterwards. If you accepted an offer that included an unfurnished accommodation, why should the company be expected to help furnish it?
Yes, it is OK to ask. Whether that would be approved or not, will depend on company policy.
Most likely, there can be some financial assistance (in form of a "loan" that you need to eventually repay at a later point of time), but there are chances of company provided one-time relocation allowance also (in-case you missed to ask).
However, you did not mention whether there was any clause in the job advertisement mentioning about "local candidate" (meaning, no relocation allowance), if that's the case, apart from the "loan" option, you're out of luck.
In addition to the answer of Sourav Gosh, you can ask for a pay in advance. For example regularly you will get your money for work in the last days of the month, but in the first month you get half (sometimes all) of it after the half month. This is an usual option in Germany, if one talk with the company about financial shortage because of relocation.
Like Sam Hanley wrote, additional money at this point is unusual. One will furnish the rooms one part after another.
(I assumed, that you need the accommodation in addition to your families place)
I think this won't be considered a very mature approach and won't be a good first impression, to ask directly for "help". Although you can ask for company policy (if you didn't receive it with the job offer) for reallocation, and if company provides some reallocation allowance, surely you'll get it. But directly presenting a need just at the time of joining the company would probably last for some long time and in case it is rejected, you'll have an awkward situation to deal with right from the start of your career in that company.