Well, I can't find a good match for the other children in 1901, unfortunately. 
Tracing Joshua the elder back, I see him in 1881 with his wife Ann and the following children: 
Ann age 6 b. Over Darwen 
Joshua age 9 b. Over Darwen
Thurston Findley age 12 b. Over Darwen. 
The reference is RG11/4208 104 12 - you can look it up for free at either 
www.familysearch.org or 
www.ancestry.co.uk We could imagine Joshua the elder is the grandfather of your Joshua. Unfortunately, none of the boys has a Norman or Leonard living with him in 1901. 
1901:  RG13/3923 38 14 
15 Duxbury Street, Darwen   Thurston Leach, head, 31, Moulder (?) Clay, b. Hoddlesden
Rhoda, wife, 31, b. Darwen 
Victoria, dau, 3, b. Darwen 
Marsden, son, 1, b. Darwen   
RG13/3921 125 28 
Darwen, 25 London Terrace  Joshua Leach, head, Sanitary pipe (sthg), b. Darwen Hoddlesden 
Alice, wife, 29, Cotton weaver, b. Bethorn 
I think you would need to get hold of Joshua's birth cert to sort out who he actually belongs to. 
FreeBMD has the following birth: 
December quarter 1894 
Registration district Blackburn 
Volume 8e page 457
I also see the births of 
Norman Leach registered in December quarter 1902 
Leonard Leach, September quarter 1901  
both in Blackburn - which would explain why I can't see them in 1901.   
Sorry I'm not able do do more for the moment. But please come back to me once you have the cert - we'll certainly be able to trace them a little further back one we have his parent's names. 
Tanja