1) HTML Embedded Object Element
You can use embed to add rich content, like videos, images, pdfs, etc.
2) Jquery load
You can use .load() when you want html, json, xml or any other content, and an advantage of .load() is that you can select wich portion of the page you would like to load.
A difference between load and embed is that you determine when the data is loaded, if you embed an object it will be loaded when the page loads (and can also cause page load issues because of that).
3) Ajax
Is behind the scenes exactly the same as .load(), but depending on the exact situation load() might be more convenient, and ajax more flexible.