"various varieties of" is correct and usable in written English.
You can use it when referring to enumerated items that are different from each other. For example: "The farmers' market offers various varieties of vegetables and fruits."
Through Sunday, "The New Auricula Theater," a showcase of dozens of auricula primroses; and "Primrose Palette," a display of various varieties of primroses.
He starred with Corbett in various varieties of sketch and cross-chat, mostly written by Barker himself under one of his pen-names.
There are various varieties of large tomatoes on the market many of which seem to have names related to cows – such as beef and oxheart.
Returning at sunset to the farm, I was greeted by Vincenzo Pitruzzello, the farmer, an ebullient host who insisted on showing me all the various varieties of oranges, picking armfuls.
The about-face followed a flood of complaints that the new design too closely resembled packaging for generic or store-brand orange juice and confused shoppers trying to tell apart the various varieties of Tropicana.
The expansion allowed the facility to refine various varieties of crude oil and more than doubled its production capacity to 600,000 barrels a day of diesel, gasoline, jet fuel and other products.
Paint workers are exposed to a various variety of harmful chemicals present in paint products such as solvents (aromatic hydrocarbons: Benzene, Toluene, and Xylene) (Roma-Torres et al. 2006).
The relative abundance of various varieties or isotopes of carbon were "consistent with a sudden and planetary die-off of plants," Dr. Ward said.
On a conservative basis, we assumed apples to weigh 100 g, although weighing of various varieties identified examples of up to 250 g (authors' measurements using household scales and a range of apples).
Beer of various varieties has been drunk for thousands of years.
At one station, people can smell the product, comparing the scents of various varieties.
