Can 使劲 (put in effort, strain at) only be used for physical effort? If no, how does its usage differ from 尽量?
使 = utilize/ apply
劲 = force / power
'使劲' as a verb means 'apply force' ; as an adverb, it means 'forcefully'; Since 'forcefully' is an adverb that modifies action verbs, it is mainly be used for describing physical effort.
For example: 使劲打(forcefully hit), 使劲拉(forcefully pull)
how does its usage differ from 尽量?
使劲 is an adverb for 'forcefully'
尽量 is an adverb for 'to the greatest extent / as far as possible'.
For example: '尽量不让人知道' (go to the greatest extent not letting people know)
'使劲' and '尽量' are not very similar in meaning
May be you were thinking of '尽力' (with all of one's strength) which can be used to describe physical effort, similar to '使劲' .
For example: '尽力打' (hit with all your might), '尽力拉' (pull with full strength)
In this sense, '使劲' and '尽力' are very similar.
But 尽力 can also be used metaphorically for 'do one's best' or 'try one's best'
For example: '尽力忍笑' (do one's best not to laugh)
Finally, '用力' (用= utilize/ use) (力 = force/strength) is synonym to '使劲'
出力 (出 = output /use) (力 = force/strength) is also a synonym