Here is the query
from a in this._addresses
where a.Street.Contains(street) || a.StreetAdditional.Contains(streetAdditional)
select a).ToList(
Check to make sure that the properties are not null
from a in this._addresses
where (a.Street != null && a.Street.Contains(street)) ||
(a.StreetAdditional != null && a.StreetAdditional.Contains(streetAdditional))
select a).ToList()
If the null check is false, then the second clause after the && will not evaluate.