You have two options depending on the actual objects in dataRow.ItemArray
If there are actually string objects in the object[] you can just cast element wise.
dataRow.ItemArray.OfType<string>().ToList();
but if the objects are of another type, like int or something else you need to convert the to string (in this example with .ToString() but another custom method might be required in your case
dataRow.ItemArray.Select(o => o.ToString()).ToList();
Edit:
If you don't need List<string> or string[] explicitly you can leave the .ToList() out and get an IEnumerable<string> instead.