Algorithm for n-of-m keys with partial results
The way I see it, you have a few options. The right one will depend on the details of the application, which are sparse in the question.


Use a stream cipher (or stream-like mode). Each party has a separate key and encrypts/decrypts with their individual key. With this you only get n-out-of-n, not m-out-of-n where $m&lt;n$.
Use MPC. You can evaluate the AES encryption/decryption circuit via MPC. It is fairly fast based on the numbers I've seen recently. Unfortunately, I don't think there is any good publicly released software out there to do this. Under this paradigm, each party would hold a share of the secret key and they would cooperatively work to do the encryption/decryption. The work I cited requires all n parties, but if the secret were originally shared with an m-out-of-n sharing scheme (like Shamir), you could convert that to an additive sharing (see this paper for a method of doing the conversion).


Some things to think about: 


Who generates the key initially?
Who is suppose to receive the output of the operations?