While it may differ from industry to industry, my experience would suggest that an organization which is soliciting social media strategies from applicants is likely composed of individuals who meet one or more of the following criteria:
(a) Have no idea what a "social media strategy" is, convinced the organization should have one
(b) Attempting to ferret out applicants who are full of hot air (i.e. any applicant who suggests that social media will revolutionize the organization's marketing capabilities)
(c) Replacing the type of applicant who promised millions of Facebook and Twitter leads ... by looking for someone else who will promise the world and perhaps has a "better" social media strategy.
Social media is not revolutionizing advertising or marketing, despite what many self-proclaimed "Social Media Strategists" tend to announce (likewise, those preaching "TV is dead" are obviously not watching the Nielsen ratings).
People don't bother with most social media advertisements (look at Facebook ads' performance) - people use social media to share their opinions on products, air their grievances, and (if you respond to their opinions or grievances) talk to your organization.
Social media is revolutionizing customer service and public relations (for those companies who are ready to engage their customers versus just talking at them).
The best strategy for maximizing one's return on time spent working with social media is to identify ways in which customers want to interact with your organization and meet them at the venue of their choice - whether that means replying to posts on their personal blogs, correcting a problem they mention on a forum, or letting them post comments to a company Facebook wall.
The tools I've found most useful for conducting the customer service and public relations side of social media have been Google Alerts (to see whenever the brand's name gets a mention) and the company's own blogs, forums, and social media profiles.