Nor would I answer them.

What is your greatest strength? Who cares, everyone expects this and practices an answer, it is hardly an accurate way to qualify an employee.

I WOULD ask;

What unique skills do you think you will bring to the table that you feel sets you apart from other applicants?

This is FAR more beneficial information to the company AND the person hiring. Anyone can download the 5 greatest strengths BS, as per your second example, but the 5 greatest strenghts crap is like asking someone WILL YOU TURN UP FOR WORK? It's canned garbage.
How about,

What 5 abilities will you bring to the company that you think we could benefit from and why?

References for the most part are a complete waste of time other than to find out if the person showed up daily and worked hard. Other than that, it is useless. I have seen very good employees get GARBAGE references due to personal conflicts or vendetta's from past employers. I worked for one company that would tell all reference inquiries that the people were constantly drunk or stoned on the job, then laugh about it to other admins. There were others who just COULDN'T tell you what people did because they were crappy managers that didn't have a clue what the person did all day anyway, but most just want off of the phone if they have been used repeatedly by a former employer, they just tire of it. Which is another reason to only offer a reference upon specific request during an interview and not with all applications. I find most employers don't bother calling references anymore anyway, too many applicants. Thus only provide references when asked and while shortlisted, otherwise you burn your own bridges.

How about offering tips for people who have no job finding skills? How about a download on how to source out and cold call potential employers? Stop emailing resume's and start arranging MEETINGS by phone and offering proposals instead of resumes? How about how people should use social networking skills to move forward in a career and not rely on certifications to do it for them?

We have hundreds of peers here that have NO job finding skills, others that actually feel you CAN'T cold call an employer and present your skills (that one still make me chuckle) and others who can't stop going to school for more courses, only to find that they have a masters in computer science and can't get a job at MacPukes. Some even believe that you MUST have certs to find a good paying IT job, it just doesn't end, people THINK so many negatives about a market, it's no wonder they remain unemployed or stuck unhappy with their present job.

As for the hiring process, HR departments don't have a clue and are the wrong people to be talking with anyway, a good meeting with the right person, (CEO or President) will never see you answering such questions to begin with. But it will get you more positive results, more money and a better job almost every time.