the meaning of 胳膊and 手臂 are the same, 胳膊＝手臂; just have a little difference; maybe just like accent in English. 胳膊often used by people in north of china; less formal, more used in daily life; 手臂often used by people in south of china; more formal, such as in articles,news; however, with the migration，the difference are weaker. so you can use any of them. can you understand me ? my english is not very well

手臂 is used in standard written Chinese. 胳膊 is used in standard spoken Chinese. They both refer to the same part of the body--the arm.

in our normal life, i think for most of us, it's same. it's just sometimes or some people will say 手臂 or 胳膊 out of their habits.

Also there is 膀子。 乔治伸出膀子，亲亲热热地搂住我的肩膀。 George affectionately put his arm around my shoulders.

In writing, you definitely want to use 手臂. In a casual conversation, it depends on the region where your listener came from(like fufufu had mentioned). And, whenever you are not sure, use 手臂 : ) at least people would understand.