How to write query to get data from other table for each columns in existing table.

You can left join three times on system_code:
select
d.id,
s_cat.full_name cat_code_full_name,
s_group.full_name group_code_full_name,
s_other.full_name other_code_full_name
from data_table d
left join system_code s_cat
on s_cat.value = d.cat_code and s.code = 1
left join system_code s_group
on s_group.value = d.group_code and s_group.code = 2
left join system_code s_other
on s_other.value = d.other_code and s_other.code = 3
To avoid repeating the joins, an alternative solution is to do conditional aggregation:
select
d.id,
max(case when s.value = d.cat_code and s.code = 1 then s.full_name end) cat_code_full_name,
max(case when s.value = d.group_code and s.code = 2 then s.full_name end) group_code_full_name,
max(case when s.value = d.other_code and s.code = 3 then s.full_name end) other_code_full_name
from data_table d
left join system_code s on s.value in (d.cat_code, d.group_code, d.other_code)
gtoup by d.id
I guess the problem you are facing here is, how to get full name for all 3 columns. 1 of the method is to join SYSTEM_CODE table thrice -
SELECT DT.ID
,SC1.FULL_NAME CAT_CODE_FULL_NAME
,SC2.FULL_NAME GROUP_CODE_FULL_NAME
,SC3.FULL_NAME OTHER_CODE_FULL_NAME
,DT.PRODUCT
FROM DATA_TABLE DT
JOIN SYSTEM_CODE SC1 ON SC1.VALUE = DT.CAT_CODE
JOIN SYSTEM_CODE SC2 ON SC2.VALUE = DT.CAT_CODE
JOIN SYSTEM_CODE SC3 ON SC3.VALUE = DT.CAT_CODE
sql-serverandoracle. Please add only the one that is relevant.