Hello. I don' t know your Japanese leve, but I hope that it will help you. Simply we use "receive something " as 「もらいます」. Ex; 「わたしは両親（りょうしん）からプレゼントをもらいました」(I received a present from my parents.) Normally「受け取ります」means to receive or get something with your hands . Ex:「 けさ、宅配便（たくはいびん）を受け取りました。」( I got a FedEx package this morning. ) Another meaning of 「受け取る」is to interpret A as B. Ex;「わたしは彼が何も言わないのをYesだと受け取りました。」(I understood his silence meant "Yes".) When we accept or welcome someone as a member of the company or group, we use 「受け入れます」. ex; 「田中さんをチームに受け入れました」(We welcomed Mr.Tanaka as a member of our team.) 「受け入れます」is also used when we adopt an idea from someone. ex:「彼のアイデアはすばらしいですが、受け入れることができません。」. (His idea is nice, but we can't accept it.) On the other hand,「引き受けます」is slightly different. 「その仕事を引き受けました」means "I accepted the job", so, 「引き受ける」is to accept some action , or carry on some action like job (and property as well) etc with your responsibility. Ex:「友だちが旅行へ行くので、彼女の犬の世話（せわ）を引き受けました。」(A friend of mine is going to travel, so I agreed to take care of her dog.) By the way, we don't use「取り受ける」much. This word is not common in our daily conversation, doesn't exist in the dictionary, I think. Some specific situation is necessary, or you have to divide it in two words. Ex;「近くにあったグローブを取り、ボールを受けました。」(I took the baseball glove beside me, and caught a ball with it.) Sorry, I don't think my English is enough. If you have a question, please write me.

I'm no master but this is my guess. 受ける by itself is "receive" When you receive something, it happens TO you. 贈り物を受けた: I received a present ^ In this case, we "recieved" the gift, maybe it came in the mail, we didn't ask for the gift, and we can't choose to "receive" it. It happened TO me. 引き受ける　is "receive/accept "but with the feeling that you CHOSE this. 引き in this kanji means "pull" +受ける means "receive" so it feels like something that YOU did. 新しい仕事を引き受けた <- I accepted the new job ^ You had the chance to take the job, or decline but you CHOSE to "receive" the job, you chose to "accept" it. I hope it helps