permit-------允许, 许可(正式用语)
We do not permit smoking in the office. 在我们的办公室里不准吸烟.
consent (to sth/do sth)------同意; 允许（也是正式用语,但是要注意＋to）
I repeat I freely consent to go with you as your fellow-missionary.我再说一遍,我爽爽快地同意跟你去,作为你的传教士的同事.
My father will never give his consent to our marriage.我父亲决不会同意我们的婚姻的.
allow--------允许, 许可(一般用语)
She allowed her mind to wander. 她任由思绪徘徊.