Let's clarify, just because you add something in the JOIN ON clause, does not mean it belongs there. Your query should be this one:
SELECT orgNm.OrgNm
FROM OrgNm orgNM
INNER JOIN ProspectClient pc ON pc.ProspectClientID = orgNm.OrgId
WHERE orgNM.OrgNmTypeId = 2
AND orgNm.OrgId NOT IN (SELECT CloneOrgId FROM ClonedOrgInfo)
AND orgnm.orgId NOT IN (SELECT RelatedOrgId FROM OrgcRlshp)
Here is one possible interpretation in three steps:
var re = from o in OrgNm
join pc in ProspectClient on o.OrgId = pc.ProspectClientID
where o.OrgNmTypeId = 2;
var ex = ClonedOrgInfo.Select(x => x.CloneOrgId).Union(OrgcRlshp.Select(y => y.RelatedOrgId));
var result = re.Where(r => !ex.Contains(re.OrgId));
Since LINQ to SQL is using deferred execution, it does not matter how many steps you use.