A number of incidents took place across the district on Wednesday afternoon between noon and 2.30pm.
In all the incidents, the suspects said they were attending from the council in response to water problems in the area.
Detective Constable Joanne Jabczynski, of Kirklees District CID, said: "Thankfully no one was injured during the incidents but it has clearly been very distressing for all the victims involved.
"It would appear the suspects have targeted older people who live alone and may appear to be more vulnerable.
"I would appeal to anyone who may have any knowledge of these incidents or may have been in or around the areas highlighted on Wednesday or may know or have seen anyone matching the suspect’s descriptions, or acting suspiciously to come forward and speak to the police."
The first incident reported was at an address on Rufford Road in Golcar, where two men entered the property at around noon.
Suspect one was described as a white man, aged 25 to 30, 5ft 8in and stocky. He wore a cap and grey zip-up top.
Suspect two was a white man, aged 22 to 25, with light coloured hair.
The suspects are believed to have used a white box type van.
The second incident was reported a short time later after three suspects entered a property on Tintern Avenue, also in Golcar.
Suspect one was described as white man, approximately 5ft 10in and of medium build, with a round face and dark eyes. He was clean shaven and wearing a dark blue cap with a peak and a dark top and bottoms.
Suspect two was a white man, slightly taller and skinnier than the first male, but wearing the same clothes.
Suspect three wore the same clothes as the other two - a dark cap and dark trousers.
The third incident, during which two men entered the address, took place on Wilson Avenue in Mirfield at around 1.35pm.
Suspect one was described as being a white man, aged around 30 to 40, around 5ft 8 inches tall and of broad build, with a fat face and no facial hair. He was wearing blue trousers, a blue top and a blue cap. He spoke with a Yorkshire accent.
Suspect two was a white man in his 40s, around 5ft 10in and slim. He had a grey hoody over his head. He had grey bottoms and spoke with an Irish accent.
The fourth incident happened at an address on New Hey Road in the Salendine Nook area of Huddersfield at around 2.30pm. Again, two men entered the address.
Suspect one was described as a white man, around 5ft 10in and skinny, with dark hair and a beard. He wore blue jeans and black anorak zipped up, and had a Yorkshire accent.
Suspect two was described as a white man, around 5ft 5in and skinny, with a ginger/blonde beard. He wore blue jeans, a grey hooded top and black gloves, and was described as having a foreign accent.
Det Con Jabczynski said enquiries into all the incidents were "very much ongoing".
She added: “If you have any concerns about the person or people attending your address, or the address of a friend or family member at any time contact the police.
"Any legitimate caller will be understanding of your checks and concerns."
Anyone with any information is asked to contact Det Cone Jabczynski or Det Sgt Coates at Kirklees CID via 101, quoting reference 13180039130.
Information can also be passed on anonymously to the independent charity Crimestoppers on 0800 555 111.