T-SQL Case Statement in a JOIN ON Clause

You're looking for IsNumeric but it doesn't always work (+,- and . are numeric) so you need to use the solution described by GBN which is to add .0e0 to your varchar

LEFT JOIN [CTSTRC] [Statuses] ON 
    (CASE WHEN ISNUMERIC(RIGHT([Statuses].[STRID], 3) + '.0e0) = 1 
          THEN  CAST(RIGHT([Statuses].[STRID], 3) AS INT) 
          ELSE 0  END) = [CTE].[F61] 

create a persisted computed column and add an index on it.

ALTER TABLE YourTable ADD
    NewIntID AS (CASE ISNUMERIC(RIGHT([Statuses].[STRID], 3) + '.0e0)
                     WHEN 1 THEN CAST(RIGHT([Statuses].[STRID], 3) AS INT) 
                     ELSE 0
                 END) PERSISTED
GO

CREATE INDEX IX_YourTable_NewIntID 
ON YourTable (NewIntID ); 
GO

you can now just join to the new NewIntID column as if it were the proper numeric ID now.

You can try to create an expression column in the Statuses table that converts the right 3 characters to a number and then try to join on the expression column.