Is there way to combine secrets first and later split them? Shamir's Secret Sharing allows a secret to be split into multiple shares so that it can be reconstructed later. 

Is there a way to do the reverse? Can we combine a few secrets first and later split them into their original forms? More clearly: given two strings I want to "pack" them into single secret and later split them into respective strings. (I'm not sure how this would be called in literature.) 

The simplest solution I could think of is concatenating all of the secrets and storing their relative positions, later string splitting them based on their positions. This would be too naive and there is no space advantage.
On the information theoretic level you can not get a shorter result than the concatenation if you want to be able to recover the original inputs: If there are $k$ shares from a set with $2^{x}$ elements (represented as $x$ bit array), an injective function requires at least $(2^{x})^k = 2^{xk}$ different function values, which requires at least $xk$ bit. If the function combining the different shares has a shorter function value, it is not injective and you can not recover the original shares.

However, since the chosen string has a specific bit representation, you might be able to work with encodings to save space, e.g. Huffman codes, etc.

You might be able to choose your common secret and shares in a way, where the shares are not compressible by much but the common secret is.