Is it possible to finish my PhD at a different institute?
My writing of the thesis will be finished soon...Is it possible to defend my work at some other institute and with another supervisor(s)? 


Do you have a supervisor in mind? If there is a particular professor who supports you, they may be able to help you navigate this and waive some of the usual requirements. 

If not, there are many issues:


Residency requirements. You generally have to be "in residence" at an institution for 1-2 years before that institution can award you a degree. So, this would put you behind schedule. 
Admission. You would effectively be a transfer student, and would have to apply for transfer admission like everyone else. This could be non-trivial: admission committees are not going to be excited about admitting a student who is already ABD somewhere else, left under less-than-good circumstances, and is eager to graduate as soon as possible. 
Letters. You've spent enough time at this institution that you will be expected to have at least one or two letters of recommendation; their absence will be suspicious. 


So: you're probably better off trying to patch things up at your current institution. If that's truly impossible, I would at least try to get a master's degree (if you don't already have one), a few good publications, and a letter of recommendation from someone at your current school before transferring somewhere else.