The official currency is the Sudanese pound (S£/SDG), which is divided into 100 piastres.
In the last couple of years the Sudanese pound has started to lose value against the US dollar at a steady rate and with inflation increasing a black market has sprung up. If you use it be very discreet. Hotels are good places to enquire. Khartoum has numerous private exchange offices which have better rates than the banks, and longer working hours. The rates offered by these offices is generally only a little lower than the black-market rate. Euros and US dollars are the easiest to change (outside Khartoum you'll be hard pressed to change anything else), though British pounds and most Middle Eastern currencies are widely accepted in Khartoum and Port Sudan. The only way to change Egyptian pounds and Ethiopian birr is on the black market, which is easy at the borders.
Money can be wired to Khartoum and Port Sudan (even from the US and UK, though this could always change because of sanctions) with Western Union and Travelex. Credit cards and travellers cheques are useless and there are no ATMs accepting foreign cards; bring all the money you might need in cash.
It's worth noting that due to international sanctions some online banking systems will block your account the moment you try and log in from Sudan. Paypal is also likely to do this (yes, we speak from experience!).