The abs light on my nissan wingroad 2004 model is constantly staying on the dash board. Also, the speedometer is not working and when I mash a sudden brakes the car swerves at the back.

SOURCE: help

It means there is a fault in the brakes/anti lock braking system. This should be immediately seen to by a mechanic. It may be best to have a mobile mechanic come, or to tow it to a service centre (might not be best to drive)

SOURCE: brake lights for nissan pulsar 1998,abs lights for same

check the fuses for the rear tail lights, check the lights, make sure they are not burnt out. (abs cable is probably not the problem, but have it changed so you know that there isn't one)

SOURCE: erratic speedometer with ABS and brakelight lit

same problem here, found 3 places that say it is the abs sensor:

Had this problem with my 1999 Ram 1500. There is a sensor at the top of the rear differential for the ABS system. That sensor went bad and replacing it took care of the problem. What caused mine to go bad was apperantly water got into the differential when launching and loading my boat. check to see if gear lube needs to be replaced also.
The answer above is perfectly correct. When the ABS sensor on the diff goes bad the speedo no longer will work, the odometer stops recording mileage and both brake and ABS light comes on. You also loose O/D or "Lock-up" in the torque converter. The sensor is inexpensive and can be changed in about 30 mins. Good Luck!

The fix for your truck is the ABS speed sensor located in the top of the differential housing , held in with one stud . Your speedometer is calculated through the ABS controller. Replacing that sensor will fix your problem.

SOURCE: ABS Ligth On constantly on the dashboard .

sounds like a dodgy ABS sensor (change both) but while your there also check the condition of your brake pads

SOURCE: Warning lights

have obd  scanner run on vehicle