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.