You do not need to be a Danish citizen in order to obtain a loan or other credit facilities from a Danish bank. Most banks offer a consultation service regarding your finances, although there is likely to be a cost for their advice.
In order to be in contention for a bank loan, the bank will need to be satisfied that you have a stable, regular income, sound finances and a fixed address in Denmark. A bank loan is probably your best option if you need extra cash at short notice.
It is important that you shop around to find the best deal for you in terms of loan prices and credit facilities, as these vary from bank to bank. The type of loan you apply for will determine your interest rate, so make sure you explore all the options available to you.
Overdrafts are available subject to an agreement between you and your bank. This is particularly advantageous if you are self-employed. The overdraft will allow you to withdraw money from your account up to an agreed limit, even if you do not have the money already in your account. However you should be aware that the interest rates on overdrafts are often very high.