This is neither trivial or easy. You can use a multi-WAN capable router, but unless your provider natively supports PPP multilink you will also need a server at the other end with sufficient bandwidth to terminate the connection. Otherwise you can only use simple load balancing between the connections which gives you, in simple terms, the ability to download four files at 7Mbps each but not one file at 28Mbps.
Furthermore if you are using the same provider with all four SIMs it is unlikely to improve speed over a single, faster device, and in any case. With a few exceptions, most modern devices are capable of using the entire capacity of most provider networks on their own, meaning multiple devices will just divide the same amount of capacity four different ways.
If it's a connection shared between multiple different users there may be more benefit to plain load balancing, but that depends on the provider. If the provider only has 2x5Mhz carriers, then a single 42Mbps modem will probably perform better than six 7.2Mbps modems.
There are lots of ways to do this with Linux - look at "Channel Bonding" for the general way to do it. Also, Zeroshell may be worth adding to your list - particularly if you have 2 boxes (ie 1 on your premises and another well connected to aggregate traffic). – davidgo – 2015-05-24T07:03:57.167