Avoiding something unpleasant or difficult:
* Dodge the bullet: To avoid something bad or dangerous.
* Steer clear of: To stay away from something or someone.
* Give something a wide berth: To avoid something or someone completely.
* Go around: To find a way to avoid something.
* Sidestep: To avoid dealing with something directly.
* Skip: To avoid something, usually something unpleasant.
Avoiding responsibility:
* Pass the buck: To blame someone else or shift responsibility.
* Shirk: To avoid responsibility or work.
Avoiding contact:
* Keep someone at arm's length: To avoid becoming close to someone.
* Ghost: To avoid someone completely, without any explanation.
* Cut someone off: To end communication with someone.
The best idiom to use will depend on the specific situation and the meaning you want to convey.