Interviews are usually pretty structured affairs, with the interviewers asking most of the questions, and the interviewees just doing their best to answer them. However, they're not like tests. There's no one right answer. There's typically no scores. Those being interviewed simply need to convince the interviewers that they are the best candidates for the job.
Therefore, you shouldn't view questions as a checklist to be checked off like if you have a passable answer to every question you'll get the job. What if someone else has a passable answer to every question too? Instead you need to figure out how you can use the questions to explain why you're the best person for the job. The questions are just a means to an end for both sides.
What do employers look for when determining who would be best? I would abstract it to three things: who can do the job, who would do the job, and who wouldn't interfere with other people doing their jobs. With each answer, you should be seeking to further your case in one of these areas.
Skill
The most important thing you need to communicate is that you are capable of doing the job. For some jobs, this might simply mean you can follow instructions, while for many it will be convincing them of your skill, knowledge, and talent.
For this, you want to be narrow and focus on experience, experience, experience. Ideally, you've done this job before and did it well. Bring that up as much as possible. Use people who witnessed such as references. Make them convinced that you can jump right in without a worry.
If you haven't done the job before, talk about the closest thing to the job you've done, and why you know how to do it. If you're new to the workforce, focus on your education in relevant areas.
Most importantly, you need to show that you know how to do that specific job. If you have been jumping between fields or doing a hobby, talking about those other fields won't convince them of your skill at this job at all. Mentioning such things can be good for the other two goals, but those are less important. If you can answer a question with an example in a relevant job, do it, even if it doesn't seem as great an answer. If they ask what your work experience, disproportionately talk about jobs in that field. If they ask you about your strengths, your strengths are things that could help at this job. If they ask what you enjoy about an unrelated job, include something that is also true about the job you are applying to. If they ask for an example of something (problem-solving, conflict resolution, etc.), use an example of something at a job in that field. Make them feel like you eat, sleep, and breathe relevant job experience.
Sometimes you may clearly be under-qualified for a job. This isn't always a death sentence for your chances though. In such a case what you need to show instead is that you're capable of learning the job quickly and with minimal hand-holding. Don't lie. In such cases, focus on recent educational achievements, other complex things you have taught yourself, and your character and hope for the best.
Character
After they feel comfortable that you can do the job, you next need convince them that you will do the job. This is where you can bring up other job experience, less relevant educational achievements, and diligent volunteer work and primarily what references are for.
How important this is depends on the job. Many entry level jobs require essentially zero prerequisite knowledge, and all they need to be sure of is that you will show up. This is why when you are new to the workforce any experience demonstrating your reliability is very beneficial. It shows that you have a proven track record of being trustworthy and hopefully a hard worker.
In more skilled professions, it is assumed that your work ethic won't be an issue. If you're applying to a more advanced position, talking about unrelated jobs which you have performed may actually be detrimental to you. It shouldn't be in doubt that you can do a job. You need to convince them that you can do this job. You shouldn't mount an uninvited defense of your character because then you're the only one putting it in question. Imagine if someone were to exposit about how they have never been convicted of any felonies out of the blue. That would hardly make him seem less suspicious. Plus, talking about unrelated skills takes away from valuable time talking about relevant skills, and it may make you seem more inexperienced or at least rusty if all you can talk about is other fields.
It's also worth mentioning that if you work in a field where you would be working with finances, sensitive information, restricted substances, or other things requiring a increase level of trustworthiness, you need to be prepared to give examples of how you've shown yourself trustworthy if possible, especially if you have a background that may make them doubt that or if you are to be lower on the totem pole.
Also, you want them to feel safe investing into you. Along with work ethic, you want to assure them that you will do the job long-term, especially if you need training. If they're going to pay to train you, they want to know you won't leave right after but that they will get a return on their investment.
Loyalty is a plus in any job. Even if you're just looking for a summer job, you want them to know you won't quit after a month. You can do this by showing prior long stints at jobs, tactfully explaining why you left jobs, and talking about your goals and how this job fits into them. Whether on a cover letter or interview, you should frame the job as the perfect fit for your skills and situation. You should seem like you love both the job and the locale. Sadly, you may have to avoid talking about your family plans or other things that may indicate a future reason to leave the job, which usually they will not ask about anyway to avoid discrimination allegations.
Personality
Finally, you need to convince them that you won't interfere with others doing their jobs and that maybe you will make it more enjoyable for them. You need to work together well. You can still talk about experience working in team, but this area is the most flexible and where soft skills are the most important. You largely just need to be likeable.
This is where you can talk about your hobbies, interests, and other things that make you seem like a good person to work with. You can talk about your family. You can talk about your conflict resolution skills. Largely, this is just about presenting yourself well and avoiding red flags. When talking about past jobs, you don't want to degrade your former employers or coworkers because it makes you seem quick to blame and bad-mouth others. You just want to seem easy-going and like you can get along with anyone.
The struggle is often that talking about things you like and are actually interested in is naturally the easiest part. However, your compatible personality should be visible in all of your conduct and speech, so this should be the least important and least focused on area. Again, it should be assumed that you are not a jerk even more than it should be assumed that you won't be a slacker. While it is important to understand the different purposes of various questions and answers, you should use this knowledge to focus your answers on the most important things. Largely, this should be the first area—your skills. Evaluate each question to answer it how to advance each area the best, but understand that not all areas are equal.