Phasal verb

get someone off可有不同的意思

第一，是去睡覺，或幫ｂｂ仔睡覺，如Cambridge Online Dictionary就有兩例：

It was so hot that I didn't get off (to sleep) till three o'clock.I've been trying to get the baby off (to sleep) for an hour!


第二，是俗語，與性有關，在此不談
第三，是避免受罰，或幫人免於受罰，字典也有一例
She was charged with fraud, but her lawyer managed to get her off.

所以，根據你的句子，就必知是第一個意思，全句是：
我已用了整個小時嘗試使嬰孩睡覺，但終告失敗，他還是搖動雙手。


至於keep off talking就如其他回答者所說，是：不要談話之意等

希望幫到你！

Jamie：
單單說(to) get the baby off 是把 BB 弄開到別處的意思, 如 get the baby off
the crowd.; get the baby off the pacifier (替 BB戒奶咀).等。
(to) keep off doing something. = (to) avoid doing something.如
keep off smoking, keep off drinking等, 所以 keep off talking就是avoid talking.
避免談話的意思。

get off = 動身, 出發,免於受罰

get the baby off = 那個嬰兒沒有受罰

2010-08-27 13:56:50 補充：
But,if you mean "get your baby off ... " ,
it should be 跟嬰兒講笑話