Oracle SQL query using case when, compacting null fields

I'm going to make the assumption that Old and New records are paired in the order they appear based on the ID value. With that assumption the following query:

WITH DTA(ID, GRP, OLD_NEW, OBJECT) AS (
  select 1, 'A', 'O', 'pen'   from dual union all
  select 2, 'A', 'N', 'house' from dual union all
  select 3, 'B', 'O', 'dog'   from dual union all
  select 4, 'B', 'O', 'cat'   from dual union all
  select 5, 'C', 'N', 'mars'  from dual union all
  select 6, 'C', 'O', 'sun'   from dual union all
  select 7, 'C', 'N', 'moon'  from dual union all
  select 8, 'C', 'O', 'earth' from dual
), dta2 as (
select dta.*
     , row_number() over (partition by GRP, old_new order by id) rn
  from dta
)
select coalesce(n.grp, o.grp) grp
     , n.object new_object
     , o.object old_object
  from (select * from dta2 where old_new = 'N') n
  full join (select * from dta2 where old_new = 'O') o
    on n.grp = o.grp
   and n.rn = o.rn;

Aside from the sample data section (with dta) this script first uses the analytic function ROW_NUMBER() to add a sequential number partitioned by the group and old_new columns. It then performs a full outer join on two inline views of the dta2 subfactored query, one for thr old objects and one for the new objects. The result, at least for this data set is:

GRP NEW_OBJECT  OLD_OBJECT
--- ----------  ----------
A   house       pen
B               dog
B               cat
C   mars        sun
C   moon        earth

In the first step assign an index (IDX) of the chnage withing your group. I'm using order by ID, but this is upon you. The important thing is that the old and new valuea are unique connected with GRP and IDX.

In next step let PIVOT work for you (I'm using the data from @Sentinel, thx!)

WITH DTA(ID, GRP, OLD_NEW, OBJECT) AS (
  select 1, 'A', 'O', 'pen'   from dual union all
  select 2, 'A', 'N', 'house' from dual union all
  select 3, 'B', 'O', 'dog'   from dual union all
  select 4, 'B', 'O', 'cat'   from dual union all
  select 5, 'C', 'N', 'mars'  from dual union all
  select 6, 'C', 'O', 'sun'   from dual union all
  select 7, 'C', 'N', 'moon'  from dual union all
  select 8, 'C', 'O', 'earth' from dual
), DTA2 as (
SELECT 
ROW_NUMBER() OVER (PARTITION BY GRP,OLD_NEW order by ID) as IDX,
GRP, OLD_NEW, OBJECT
from DTA
)
select * from DTA2
PIVOT (max(OBJECT) OBJECT  for (OLD_NEW) in 
('N' as "NEW",
'O' as "OLD"
))
order by GRP;

result

IDX, GRP, NEW_OBJECT, OLD_OBJECT
1   A   house   pen
1   B           dog
2   B           cat
2   C   moon    earth
1   C   mars    sun

Here's an alternative using PIVOT to get the results:

with items as (select 1 id, 'A' grp, 'O' old_new, 'pen' obj from dual union all
               select 2 id, 'A' grp, 'N' old_new, 'house' obj from dual union all
               select 3 id, 'B' grp, 'O' old_new, 'dog' obj from dual union all
               select 4 id, 'B' grp, 'O' old_new, 'cat' obj from dual union all
               select 5 id, 'C' grp, 'N' old_new, 'mars' obj from dual union all
               select 6 id, 'C' grp, 'O' old_new, 'sun' obj from dual union all
               select 7 id, 'C' grp, 'N' old_new, 'moon' obj from dual union all
               select 8 id, 'C' grp, 'O' old_new, 'earth' obj from dual)
-- end of mimicking your items table with data in it. See SQL below:
select grp,
       new_object,
       old_object
from   (select grp,
               old_new,
               obj,
               row_number() over (partition by grp, old_new order by id) rn
        from   items)
pivot (max(obj)
        for old_new in ('N' new_object,
                                'O' old_object))
order by grp,
         rn;

GRP NEW_OBJECT OLD_OBJECT
--- ---------- ----------
A   house      pen       
B              dog       
B              cat       
C   mars       sun       
C   moon       earth     

Provided that

• there's at most one new object for each old,
• there's no new object without old object, and
• there's at most one old object for any group (this is not true for your sample data, but in comments you indicate you're interested in such solution as well)

a simpler query may be used than for the general case:

select
    old.group as group, new.object as new_object, old.object as old_object
from
    (select group, object from my_table where old_new = 'O') old
        left join
    (select group, object from my_table where old_new = 'N') new
        on (old.group = new.group)