To make this easier, you can define 2 dateTime variables outside the linq query to represent the startOfWeek and endOfWeek values.
Then in the Linq query you can have 2 predicates to check whether the client birthday falls between the start and end dates.
Also you can use DateTime.DayOfYear to make the comparison easier.
(Edit)
Using a Northwind example, the follwoing code should work:
var startDate = DateTime.Now;
var endDate = DateTime.Now.AddDays(7);
var q = from emp in metaData.Employees
where emp.BirthDate.Value.DayOfYear >= startDate.DayOfYear
&& emp.BirthDate.Value.DayOfYear <= endDate.DayOfYear
select emp;
Unfortunatly running this code today will bring back no results, as there are no emplyees in the northwind with a birthday in the next 7 days.
But to make sure it's working, use HireDate instead of the BirthDate and you shall get 2 employees back