How do I find the cumulative distance between geometry points in SQL Server 2014?
OK, then this is the query, SQL Server 2012+ . I'll use test data instead of your query and omit all customer, order details but orderid. The query also doesn't use spatial features which doesn't help much here as we use no geography but plain geometry distance.

with points as(
select orderid, id, Coord_X, Coord_Y,
    rn = ROW_NUMBER() OVER(PARTITION BY orderid ORDER BY SQUARE (t.Coord_X) + SQUARE (t.Coord_Y) DESC)
from (
    values 
        (1, 1, 10, 20), 
        (1, 2, 15, 30), 
        (1, 3, 25, 5),
        (2, 1, 15, 20), 
        (2, 2, 17, 30), 
        (2, 3, 27, 8)
    ) t(orderid, id, Coord_X, Coord_Y)
)
select pfr.orderid, pfr.rn, pfr.id, pto.id,
    dist = SQRT(SQUARE(pfr.Coord_X - pto.Coord_X) + SQUARE (pfr.Coord_Y - pto.Coord_Y)),
    cumdist = SUM(SQRT(SQUARE(pfr.Coord_X - pto.Coord_X) + SQUARE (pfr.Coord_Y - pto.Coord_Y)))
        OVER (PARTITION BY pfr.orderid ORDER BY pfr.rn)
from points pfr
join points pto on pto.orderid = pfr.orderid and pto.rn=pfr.rn+1


May I say that this cumdist is far from being shortest in many cases.

Trying to use the second query from the question as a data source, not tested:

with points as(
select orderid, id, Coord_X, Coord_Y,
    rn = ROW_NUMBER() OVER(PARTITION BY orderid ORDER BY SQUARE (t.Coord_X) + SQUARE (t.Coord_Y) DESC)
from (
   -- data source
    SELECT odrerid = 1, -- the data source returns single transportation order or route i suppose
        id = t_Addresses.ID -- probably you have it. It is intended to be a separate id for every point to be visited
        Coord_X = t_Addresses.Coord_X, 
        Coord_Y = t_Addresses.Coord_Y 
    FROM t_Addresses 
    WHERE t_Addresses.Cust_ID IN (
            SELECT DISTINCT t_Orders.Cust_ID 
            FROM t_Orders 
            WHERE t_Orders.Del_Date='2016-05-21' AND t_Orders.Del_Sess=1) 
        AND ( (t_Addresses.Coord_Y &gt;= 0 AND t_Addresses.Coord_X &lt;= 0 AND SQUARE(t_Addresses.Coord_X) &lt; SQUARE(t_Addresses.Coord_Y)) 
           OR (t_Addresses.Coord_Y &gt;= 0 AND t_Addresses.Coord_X &gt;= 0 AND (t_Addresses.Coord_X) &lt; (t_Addresses.Coord_Y)) )
    --    
    ) t
)
select pfr.orderid, pfr.rn, pfr.id, pto.id,
    dist = SQRT(SQUARE(pfr.Coord_X - pto.Coord_X) + SQUARE (pfr.Coord_Y - pto.Coord_Y)),
    cumdist = SUM(SQRT(SQUARE(pfr.Coord_X - pto.Coord_X) + SQUARE (pfr.Coord_Y - pto.Coord_Y)))
        OVER (PARTITION BY pfr.orderid ORDER BY pfr.rn)
from points pfr
join points as pto on pfr.orderid = pto.orderid and  pto.rn=pfr.rn+1


I also changed the WHERE to: 

WHERE t_Addresses.Cust_ID IN (..) AND ( (..) OR (..) )


My guess is you need proper Cust_ID AND points within a quadrant.

I made some assumptions, please correct me if they are wrong.