They look like they all run on the same frequency, so they should be able to run together. You would have to make sure, however, that you run it in some way that allows all of the transmitters to share the connection without drowning each other out. Synchronizing these would be difficult, so you may need to have each transmitter also have a receiver. It looks like they come together anyway, so I don't think you'd be wasting money.
I'm no expert, and I didn't look at how it works too closely, but it looks as if the TX/RX modules don't really concern themselves with sending data; they just make a "virtual wire" for extending connections. So what you need is a connection protocol that will allow for multiple sensors to civilly report their readings and synchronize themselves. Something like SPI or I2C would work, but they require multiple wires, so it's out.
The Arduino's serial connection uses one transmitter (TX) and one receiver (RX) line to establish two-way communication, which can (I think) use the transmitter and receiver part of your RF modules. This could be the way to go, but I don't know whether it's possible for multiple devices to use the same connection. If it's possible to just broadcast a "Calling Sensor 7" message and have only Sensor 7 respond, then this would work. However, I am guessing (and I don't know) that there is some sort of handshaking that has to go on to establish this connection, so having multiple devices all share the same connection might be hard, because they might all try to respond to any message sent. Your job, then, would be to learn more about the serial protocol (UART) and figure out whether multiple devices could listen and chime in. In the likely case that that's not possible, you would either have to find another existing protocol or roll your own. With the hardware, it should be possible.
One last thing: you'll almost certainly want to have an Arduino on the receiving end instead of a Pi. Pi's are usually terrible at timing-critical things like communications protocols, so it would be a lot easier for you to have one more Arduino to act as the master and receive all the data and then send it to the Pi over a USB connection.
This is as much as I can offer; I don't think I know enough to do it myself, but I wanted to point you in the right direction. Good luck.
PS—Look at this question, if you haven't already.
{node:x123, temp:yyy, humid:zzz, more:123, evenmore, abc}and send it as plan ASCII in the air. JSON is built to be human readable, lightweight and easy to compress!