To glue Plexi to itself there is a clear liquid - acid weld - (Methylchoride) that works great. Just need a well vented area and not get any on your skin. You can use a small artist brush to apply and it bonds in seconds.
To glue plexi to PVC or Styrene - Goop (flexible joint), epoxy (rigid joint) or plastic cement.
When gluing Acrylic to Acrylic, you want to use Acrylic Solvent Cement. You can buy that product at TAP Plastics. Also on the TAP Plastics website are videos showing the techniques required to get good, strong glue joints. You can access the videos using this Video Link. There is one called "How to Glue Acrylic" and another "How to Build a Box with Plastic". The Acrylic Cement will also bond the Styrene to the Acrylic. My experience has shown that you can achieve a stronger bond if you add a little MEK into the solvent cement just before you use it. The MEK does the best job of bonding Styrene to Styrene. If you do not like using the water thin Acrylic Cements, then I recommend using Weld-On 16. Weld-On 16 has a consistency of syrup and will fill small gaps. It contains MEK along with the regular Acrylic Solvent Cement that is mostly Methylene Chloride. The Weld-On #16 is a great glue to have in your tool box as it works extremely well on most solvent weldable plastics; including Styrene, ABS and Acrylic.
You may notice that I use the word Acrylic instead of the word Plexiglass. PlexiGlas is a trade name for acrylic plastic. Other trade names are Lucite, Perspex, Acrylite and ChemCast. They are all bacically the same thing, Methyl Methacrylate Monomer ... or as we know it ..Acrylic Plastic.