The hundreds of bags, which the council says contain "unidentified content", have appeared on a site in Bowbridge Road, Newark over the past month.
Residents say the pile is now about 10ft (3m) high and 100ft (30m) wide.
Newark and Sherwood District Council said it was talking to the Environment Agency about removing the bags.
Glenys Moorhouse, who lives directly opposite, said: "It's disgusting, especially when it starts to smell, and when the summer gets here we might get rats or mice."
Andrew Else said: "It's not very pleasant at all. No-one seems to know why it's suddenly happened. It just appeared one day."
Tony Roberts, ward councillor and chairman of the council's leisure and environment committee, said some of the bags appeared to contain matter similar to insulation material.
"It looks unsightly," he said
"There's an awful lot of rubbish, whatever that rubbish is.
"It could contain potentially contaminating rubbish and that's the difficulty. It's a big mystery where they have come from."
Newark and Sherwood District Council said it had called an urgent meeting with the Environment Agency "to bring about a quick resolution".
An Environment Agency representative said: "We are investigating the situation and need to be satisfied that the operators are taking all appropriate measures to manage odours."
They said enforcement action would be taken if necessary.
A mountain of rubbish bags left dumped on derelict land in Nottinghamshire has sparked a council probe into where the refuse came from.