Is it normal to wire money or give cashiers check to my attorney account the day before closing the deal?

You did not post the type of deal to which you are referring, but it's likely fine.

Impossible to say what the nature of your relationship is or why you are being asked to do this. Please clarify and repost. Thank you

You need to provide more information on the type of deal and the nature of the relationship, but this type of thing happens in certain situations.

Probably not. It depends on what type of case you have and the circumstances. If you are dealing with a reputable law firm or attorney-someone known in the community who has been in business for a while, it should be OK. If this is a real estate closing, and you are the buyer, it doesn't sound that unusual.