They can't sack you for no reason. If they do sack you, they will need to compensate you money. Refer to your original offer letter. There should state some of the compensation of this type.

Tell the HR that you did some research and ask around then mention to them that the so called "reasons" they gave you are no valid enough. If you don't feel comfortable signing them, then don't sign. I guess if in the end they do sack you, I will not consider it as a bad thing. Since it's very unprofessional for a MNC company to behave that way. You might want to consider your career prospect in there. If there's anything not legal, you can sue them. Additionally, if the MD went for 3 weeks holiday, tell them you will only sign after having a discussion with the MD to get a proper reason from him/her.