If your diploma engineering is of atleast 3 years then yes you can do MBA. Work experience is not mandatory but as you have a good work experience so it will act as a plus point for you during the admission in any MBA college and even later in the next 2 years when you will be pursuing MBA degree.

For pursuing MBA you need to appear in the MBA exams like CAT, XAT, MAT, CMAT, SNAP and NMAT. You can appear in one or all the MBA exams there is no restriction regarding that. More exams open more college choice for you. Then after the result, you will need to apply to different colleges where you think have a good chance of getting called for second round of GD and interview. After going through second round if you stand on the merit list then you will get the admission.

It's a long hectic procedure but you will get to know about it in detail once you start your preparations for the MBA exams which is the first step and the most difficult step.