apache 2.2 - Website performance sluggish - High CPU and Disk Usage

Over the past couple of days my website's performance has been very sluggish, with queries taking a lot of time to execute. My CPU usage hit around 100% 4 times this week. Here is the output of top at one such time

top - 00:08:03 up 3 days, 21:47,  2 users,  load average: 6.06, 1.95, 0.84
Tasks:  92 total,   2 running,  90 sleeping,   0 stopped,   0 zombie
%Cpu(s): 86.1 us, 12.9 sy,  0.0 ni,  0.0 id,  0.0 wa,  1.0 hi,  0.0 si,  0.0 st
KiB Mem:   1017948 total,   773520 used,   244428 free,   107200 buffers
KiB Swap:        0 total,        0 used,        0 free.   257228 cached Mem

  PID USER      PR  NI    VIRT    RES    SHR S %CPU %MEM     TIME+ COMMAND
28433 www-data  20   0  854660  69288   5608 S 98.7  6.8   0:47.36 apache2
28469 www-data  20   0  529692   7692   3012 S  0.7  0.8   0:00.13 apache2
28514 root      20   0   24820   1488   1064 R  0.7  0.1   0:00.08 top

   25 root      20   0       0      0      0 S  0.3  0.0   1:00.70 kworker/0:1
28518 postgres  20   0  370016   6984   4276 S  0.3  0.7   0:00.01 postgres
    1 root      20   0   33384   1288      0 S  0.0  0.1   0:11.70 init
    2 root      20   0       0      0      0 S  0.0  0.0   0:00.13 kthreadd
    3 root      20   0       0      0      0 S  0.0  0.0   0:09.40 ksoftirqd/0
    5 root       0 -20       0      0      0 S  0.0  0.0   0:00.00 kworker/0:0H
    7 root      20   0       0      0      0 S  0.0  0.0   0:45.06 rcu_sched
    8 root      20   0       0      0      0 R  0.0  0.0   1:54.47 rcuos/0
    9 root      20   0       0      0      0 S  0.0  0.0   0:00.00 rcu_bh
   10 root      20   0       0      0      0 S  0.0  0.0   0:00.00 rcuob/0

   11 root      rt   0       0      0      0 S  0.0  0.0   0:00.00 migration/0 

Apache seems to be taking up a lot of CPU but I have no idea why. It was working perfectly up until a couple of days ago. I've optimized Apache by removing unused modules, tuned it to only have a small number of spare children running but that doesn't seem to have made a difference. I've also installed mod-evasive and mod-qos to protect against DDOS. Here is my apache configuration

Timeout 30
KeepAlive On
MaxKeepAliveRequests 100
KeepAliveTimeout 5



    StartServers          1
    MinSpareServers       1
    MaxSpareServers       3
    MaxClients           10
    MaxRequestsPerChild 3000



    StartServers          1

    MinSpareThreads       5
    MaxSpareThreads      15 
    ThreadLimit          25
    ThreadsPerChild       5
    MaxClients           25
    MaxRequestsPerChild 200



    StartServers          1

    MinSpareThreads       5
    MaxSpareThreads      15 
    ThreadLimit          25
    ThreadsPerChild       5
    MaxClients           25
    MaxRequestsPerChild 200



    MS_METHODS POST,PUT,OPTIONS,CONNECT 

    MS_WhiteList /etc/spamhaus.wl 
    MS_CacheSize 256 

Here is my VirtualHost configuration

    RewriteEngine On

    RewriteCond %{HTTP_HOST}  ^example.com [nocase]
    RewriteRule ^(.*)         http://www.example.com$1 [last,redirect=301]

    ServerName example.com
    ServerAlias www.example.com
    ServerAdmin admin@example.com

    WSGIDaemonProcess example python-path=/home/abc/example:/home/abc/example/env/lib/python2.7/site-packages
    WSGIProcessGroup example
    WSGIApplicationGroup %{GLOBAL}

    WSGIScriptAlias / /home/abc/example/wsgi.py

    DocumentRoot /home/abc/example

    
        Require all granted
    

    Alias /static/ /home/abc/example/static/


    
        Order deny,allow
        Allow from all
    

    Alias /media/ /home/abc/example/media/

    
        Order deny,allow
        Allow from all

    

    ErrorLog ${APACHE_LOG_DIR}/error.log
    CustomLog ${APACHE_LOG_DIR}/access.log combined

Here is my .htaccess file

Header set Cache-Control "max-age=31536000, public"



Header set Cache-Control "max-age=604800, public"



    AddType application/javascript          js

    AddType application/vnd.ms-fontobject   eot
    AddType application/x-font-ttf          ttf ttc
    AddType font/opentype                   otf
    AddType application/x-font-woff         woff
    AddType image/svg+xml                   svg svgz 
    AddEncoding gzip                        svgz



    AddOutputFilterByType DEFLATE text/html text/plain text/css application/json

    AddOutputFilterByType DEFLATE application/javascript
    AddOutputFilterByType DEFLATE text/xml application/xml text/x-component
    AddOutputFilterByType DEFLATE application/xhtml+xml application/rss+xml application/atom+xml
    AddOutputFilterByType DEFLATE image/x-icon image/svg+xml application/vnd.ms-fontobject application/x-font-ttf font/opentype

I'm using memcached to cache most of the queries. Web pages with few basic queries are faster (still not as fast as before though) while pages with complex queries take a lot of time. The server response time for such pages has increased from 0.2 seconds to 4 seconds (measured using Google PageSpeed Insights).

I'm using a PostgreSQL 9.3 database. Following is my postgresql.conf tuned using PgTune.

default_statistics_target = 50
maintenance_work_mem = 60MB
constraint_exclusion = on
checkpoint_completion_target = 0.9
effective_cache_size = 704MB
work_mem = 6MB
wal_buffers = 8MB
checkpoint_segments = 16
shared_buffers = 240MB

max_connections = 80

Here is the graph of CPU, Disk and Bandwidth usage over the past month

Though the bandwidth shows an increase in the past week or so, but the actual traffic hasn't increased. I am getting an average of 1500 visitors per day for the past 15-20 days. The increased bandwidth usage could probably be an increase in bot activity.

My website is a Django application hosted on droplet with the configuration - 1GB Ram, 30GB SSD Disk, Ubuntu 14.04 x64. I have tried every possible thing I could think and cannot for the life of me figure out what's wrong here. I am not very good at handling servers and the only thing I can think of now is to switch from Apache to nginx and from PostgreSQL to MySQL. Any suggestions that can help me figure out how to fix this would be greatly appreciated.