London Hostels

From my experience, you really can't go wrong with any YHA hostel. They are all similar in cleanliness and how they are run. If it has the YHA label you can be pretty sure it's going to be fine as hostels go. I've stayed in quite a few and haven't found a bad one.
All of these locations are in central London and are not far from public transport. Really, all you are looking for is an inexpensive place to lay your head at night and a breakfast to get you going in the morning. Any of these would be fine.
What I would do is list everything you want to see and do in London and then see which hostel is the most central to those. If a self-catering kitchen is important to you then you should pick one of those three...again, they are all quite central and close to public transport.

The London attractions are all spread out, so you will need to use public transport, so all your options would be suitable. Earl's Court is further out and St Paul's is in the City (CBD) so will be quieter at the weekend, although there is St Paul's, Borough Market (not Sundays) and the South Bank to cover from here.

I would go for Oxford St or Central. Book early for the best deals.

Jennifer, why would you choose Oxford St or Central?

I don't want to highjack the thread, but I have always thought hostels were very noisy and full of very young partying people. I am 51 and wonder if a hostel would be right for me. I like the idea of self-catering.

I'm 45 and was in my early 40s when I stayed in a hostel the first time -- which was the DC Hostel International. I loved it, which is saying something as a private and rather introverted person.

The guests were all sorts from all walks of life and that first time there were a lot of kids from Japan and China, a couple families from Germany and several retirees from Spain. It was quiet and peaceful and I never felt bothered. Everyone was respectful.

I have learned that each hostel is has a different character and it works to scope them out. Ones that talk about their nightlife are probably where you'll find the parties, while those that talk about the family friendly atmosphere are more likely quiet. I also stick to those associated with Hostel International/Youth Hostel Association.

The party hostel to avoid in London is called "The Generator". It is known to young tourists as a party-all-night hostel.

The YHA hostels above are not like that. They would all be fine for a stay for a person of any age. Yes, Sandra, these would all be fine for you. They all have what is called a "Family Room". But if you are traveling solo or with a friend, you could still reserve a family room. More privacy, because no one else stays in the room with you. The other rooms in hostels have 6 to 8 bunk or twin beds, and any number of strangers might be assigned the same room as you. Not much difference in price between the two room types.