Your blog is hosted on blogger so WordPress specific solutions don't apply to you. The below methods can be usd to post the blog update on Facebook, Facebook pages, Google Plus and Twitter.
Here are some ways to automate the blog posting to social media.
1. Sign up for Dlvr.it
2. In free plan, you may find one option where you can use your blog feed to automate on social media.
3. Add your RSS feed of the blogger.
4. Add the social media sites. Free plan has option to add 3 sites.
5. Authenticate the sites you want to auto post.
6. Choose the sites for your feed.
7. Save settings.
Do take note that it takes a few minutes to hours for blogger feed to trigger the dlvr it or any other automation tool. So you have to be patient for the content automation.
Another alternative is to this process is IFTTT. This tool allows you to automate social media based on trigger. Here you can set the trigger.
1. Read the feed for updates.
2. If there is new post.
3. Send the feed post to the social media.
4. Save the automation.
Do note that IFTTT takes some time to get used to. So try using this with some experimentation.
This is similar to the IFTTT. Here you can set the workflow the same way to that of the IFTTT. You can use multiple social networks through zapier. But free plan has it's limitations. But here tthe triggers are pretty much the same.
1. Read your updated blog feed from blogger.
2. If new post exist send the trigger to social media.
3. Post update on social media.
These three are more than enough for your blog automation for social media requirement.