How can I write a strong literary analysis on Romeo and Juliet and what are some suggestions on picking literary aspects?

The key to a strong literary analysis is a strong, clear, and concise thesis statement.  It is going to guide every part of your analysis.  The thesis needs to be more than a statement of fact.  It needs to include an opinion that you are going to argue using the text as support.  For example, a terrible thesis would be "Romeo is a young boy."  There is nothing to argue there.  That is a statement...

The key to a strong literary analysis is a strong, clear, and concise thesis statement.  It is going to guide every part of your analysis.  The thesis needs to be more than a statement of fact.  It needs to include an opinion that you are going to argue using the text as support.  For example, a terrible thesis would be "Romeo is a young boy."  There is nothing to argue there.  That is a statement of fact.  A possible thesis about Romeo might be "Although Romeo appears to be in love with Juliet, he is more in love with the idea of being in love."  That gives you something to argue.  One more suggestion about the thesis.  Make it super specific.  A broad thesis is a vague thesis.  It tells the reader that you really don't have a clear idea of what you are arguing.  The more specific your thesis, the more dialed in you can get your argument and support.  

Your question asked for some suggestions on what to pick for your analysis of Romeo and Juliet.  Themes are always good to analyse.  You could pick the theme of love, but that might be overdone at this point.  I always like reading student essays that analyze and compare and contrast Romeo's relationship with his family to Juliet's relationship with her family.  If you don't want to analyze a theme, then you could do a character analysis.  Take Friar Lawrence for instance.  Is he a good or evil character?  It could be argued that without Friar Lawrence, Romeo and Juliet would still be alive.  You could do a close analysis of the nurse.  She is all over the place.  One minute she is encouraging Juliet to be with Romeo, and the next minute she tells Juliet to marry Paris.  Whatever topic that you choose, be sure to use plenty of quoted text to support.  That will really secure the point that you are trying to make.