They said the city has been without electricity for two days.
A taxi driver reported the price of petrol at 50 Sudanese pounds ($7) a gallon (4.5 litres), or about four times the price in the capital Khartoum.
Fuel reaching Nyala is subject to attack during its overland journey across Darfur.
Despite the tensions, people are trying to carry on with their lives.
Students were in the streets walking to and from school.
A main market in the town was operating.
But another commercial area remains shut after it was burned and looted on Sunday, as residents ran for their lives during fresh fighting.
That same day Ali Kushayb, a former commander of the Janjaweed, was left wounded during an attack which reportedly killed two of his men, local sources said.
Kushayb is wanted by The Hague-based International Criminal Court for crimes against humanity and war crimes allegedly committed earlier in the Darfur conflict.
Security has worsened in Darfur this year, the United Nations says.
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