How do you create a conditional count across multiple fields?

I have the huge table of over 100 million rows of data which is joined to another reference table that I want to create a conditional count for.

The first table is the large one which is an audit log and contains data which lists data on countries and contains a date of audit. The second table is a smaller table which contains relational data to the audit log. The first part is the easy bit which is to identify which audit data I want to see. I have the following code to identify this:

    select aud.*
    from audit_log aud
    join database db on db.id=aud.release_id
    where aud.event_description like '% opted in'
    and r.creation_source = 'system_a'

This gives me the data in the following format:

Country             Event Description                                   Audit Date
Czech Republic      Czech Republic has been automatically opted in      11-AUG-14 07.01.52.606000000
Denmark             Denmark has been automatically opted in             12-AUG-15 07.01.53.239000000
Denmark             Denmark has been automatically opted in             11-SEP-15 07.01.53.902000000
Dominican Republic  Dominican Republic has been automatically opted in  11-SEP-15 07.01.54.187000000
Ecuador             Ecuador  has been automatically opted in            11-DEC-14 07.01.54.427000000
Ecuador             Ecuador has been automatically opted in             11-NOV-14 07.01.54.679000000

The number of results from this query still returns over 5 million rows so I cannot export the data to Excel to create a count. My two main issues are the number of rows and the date format of the 'Audit Date' field.

Ideally I want to create a count which shows the data as:

Country                |Aug-14|Nov-14|Dec-14|Aug-15|Sep-15
Czech Republic         |  1   |      |      |      |
Denmark                |      |      |      |  1   | 1
Dominican Republic     |      |      |      |      | 1
Ecuador                |      | 1    |  1   |      |        

Any idea's on how I extract the month and year and drop the figures into column by country?

Thanks

Edit - Thank you xQbert for you solution, it worked perfectly! The problem now is that I have run into a new problem. I need to constrain the count by another query, but there is no unique identifier between the tables involved.

For example, I amended your query to fit my db:

select cty.country_name, 
SUM(CASE WHEN to_char(Audit_Date,'MON-YYYY') ='AUG-2014' then 1 else 0 end) as "AUG-14",
SUM(CASE WHEN to_char(Audit_Date,'MON-YYYY') ='SEP-2014' then 1 else 0 end) as "SEP-14",
SUM(CASE WHEN to_char(Audit_Date,'MON-YYYY') ='OCT-2014' then 1 else 0 end) as "OCT-14",
SUM(CASE WHEN to_char(Audit_Date,'MON-YYYY') ='NOV-2014' then 1 else 0 end) as "NOV-14",
SUM(CASE WHEN to_char(Audit_Date,'MON-YYYY') ='DEC-2014' then 1 else 0 end) as "DEC-14",
SUM(CASE WHEN to_char(Audit_Date,'MON-YYYY') ='JAN-2015' then 1 else 0 end) as "JAN-15",
SUM(CASE WHEN to_char(Audit_Date,'MON-YYYY') ='FEB-2015' then 1 else 0 end) as "FEB-15",
SUM(CASE WHEN to_char(Audit_Date,'MON-YYYY') ='MAR-2015' then 1 else 0 end) as "MAR-15",
SUM(CASE WHEN to_char(Audit_Date,'MON-YYYY') ='APR-2015' then 1 else 0 end) as "APR-15",
SUM(CASE WHEN to_char(Audit_Date,'MON-YYYY') ='MAY-2015' then 1 else 0 end) as "MAY-15",
SUM(CASE WHEN to_char(Audit_Date,'MON-YYYY') ='JUN-2015' then 1 else 0 end) as "JUN-15",
SUM(CASE WHEN to_char(Audit_Date,'MON-YYYY') ='JUL-2015' then 1 else 0 end) as "JUL-15",
    SUM(CASE WHEN to_char(Audit_Date,'MON-YYYY') ='AUG-2015' then 1 else 0 end) as "AUG-15",
    SUM(CASE WHEN to_char(Audit_Date,'MON-YYYY') ='SEP-2015' then 1 else 0 end) as "SEP-15"
    from dschd.audit_trail aud
    join dschd.release r on r.id=aud.release_id
    join dschd.country cty on aud.EVENT_COUNTRY_ID=cty.id
    where aud.event_description like '% opted in'
    and r.creation_source = 'DSCHED'
    GROUP BY cty.COUNTRY_name

My second query is:

select  *
from DSCHD.RELEASE_COUNTRY_RIGHT rcr
join dschd.release r on rcr.RELEASE_ID=r.ID
join dschd.country cty on rcr.COUNTRY_ID=cty.id
where r.release_status in ('DRAFT', 'SCHEDULED', 'FINAL', 'DELIVERED')
and r.is_active = 'Y'
and rcr.MARKETING_RIGHT = 'Y'
and rcr.OPT_OUT = 'N'
and r.creation_source = 'DSCHED'

The problem is that I have many countries which can relate to one ID (Release_ID) but there is no unique identifier between the tables on a country level. Each country has an ID though.

So for query 1, to identify each unique row I would need the 'aud.Release_ID' and the 'aud.Event_country_id' and for query 2 to achieve the same I would need to use the 'rcr.Release_ID' and 'rcr.country_id'.

select cty.country_name, 
SUM(CASE WHEN to_char(Audit_Date,'MON-YYYY') ='AUG-2014' then 1 else 0 end) as "AUG-14",
SUM(CASE WHEN to_char(Audit_Date,'MON-YYYY') ='SEP-2014' then 1 else 0 end) as "SEP-14",
SUM(CASE WHEN to_char(Audit_Date,'MON-YYYY') ='OCT-2014' then 1 else 0 end) as "OCT-14",
SUM(CASE WHEN to_char(Audit_Date,'MON-YYYY') ='NOV-2014' then 1 else 0 end) as "NOV-14",
SUM(CASE WHEN to_char(Audit_Date,'MON-YYYY') ='DEC-2014' then 1 else 0 end) as "DEC-14",
SUM(CASE WHEN to_char(Audit_Date,'MON-YYYY') ='JAN-2015' then 1 else 0 end) as "JAN-15",
SUM(CASE WHEN to_char(Audit_Date,'MON-YYYY') ='FEB-2015' then 1 else 0 end) as "FEB-15",
SUM(CASE WHEN to_char(Audit_Date,'MON-YYYY') ='MAR-2015' then 1 else 0 end) as "MAR-15",
SUM(CASE WHEN to_char(Audit_Date,'MON-YYYY') ='APR-2015' then 1 else 0 end) as "APR-15",
SUM(CASE WHEN to_char(Audit_Date,'MON-YYYY') ='MAY-2015' then 1 else 0 end) as "MAY-15",
SUM(CASE WHEN to_char(Audit_Date,'MON-YYYY') ='JUN-2015' then 1 else 0 end) as "JUN-15",
SUM(CASE WHEN to_char(Audit_Date,'MON-YYYY') ='JUL-2015' then 1 else 0 end) as "JUL-15",
    SUM(CASE WHEN to_char(Audit_Date,'MON-YYYY') ='AUG-2015' then 1 else 0 end) as "AUG-15",
    SUM(CASE WHEN to_char(Audit_Date,'MON-YYYY') ='SEP-2015' then 1 else 0 end) as "SEP-15"
    from dschd.audit_trail aud
    join dschd.release r on r.id=aud.release_id
    join dschd.country cty on aud.EVENT_COUNTRY_ID=cty.id
    where aud.event_description like '% opted in'
    and ***** in (select  ******
                 from DSCHD.RELEASE_COUNTRY_RIGHT rcr
                 join dschd.release r on rcr.RELEASE_ID=r.ID
                 join dschd.country cty on rcr.COUNTRY_ID=cty.id
                 where r.release_status in ('DRAFT', 'SCHEDULED', 'FINAL', 'DELIVERED')
                 and r.is_active = 'Y'
                 and rcr.MARKETING_RIGHT = 'Y'
                 and rcr.OPT_OUT = 'N'
                 and r.creation_source = 'DSCHED')
GROUP BY cty.COUNTRY_name

The bit I am stuck at are the two parts which are indicated by '*****' as the join criteria is two fields.

Any ideas?