Assuming you already have .NET domain types for your tables:
IQueryable<OtherCharges> otherCharges = ...
Guid otherKey = ...
var query = otherCharges.Where(oc => oc.OtherKey == otherKey)
.Select(oc => new { oc.ChangeItem, oc.Value })
.GroupBy(t => new { t.ChangeItem.ChangeGroup.Code, t.ChangeItem.ChangeType })
.OrderBy(g => g.Key.Code)
.ThenBy(g => g.Key.ChangeType)
// note that if Code is a non-nullable type you'll want to cast it to int? at some
// point so that when pulled into memory EF won't complain that you can't cast
// null to a non-nullable type. I expect that Code could sometimes be null here
// do to your use of LEFT OUTER JOIN in the T-SQL
.Select(g => new { g.Key.Code, g.Key.ChangeType, Sum = g.Sum(t => t.Value) });
var inMemoryResult = query.ToList();
Note that I'm using OtherCharge.ChangeItem and ChangeItem.ChangeGroup here. These are association properties and need to be set up as part of your model (e. g. using fluent configuration for EF code first).