I want to know if there is any way to communicate users without internet connection to a server.
I thought it might be possible through SMS and machine-readable encoding. However this question confirms that iOS apps allows sending but not reading SMS: iphone app reading sms
I've also read a lot about using USSD but it seems that mobile opened messages aren't possible in iOS (dial USSD code from iphone programatically) and while in Android is possible to call a code programatically there is no USSD API to, nor it's possible to send USSD messages silently.
Is there any way to transfer data between my app and my server with only basic voice-sms signal?
You are correct that SMS could be used to communicate with the server, if the server has access to a GSM modem. For large volumes of SMSes, you'd expect to have an internet connection between your server and an SMS gateway that connects directly to the messaging centre in the mobile network, instead of a modem.
This is the model of the SMS voting servers.
You can send/receive SMS as long as you have a GSM network, and you're right; no IP connection is needed. The Android platform lets you send and receive SMSes - see here.
Disadvantages are that SMS can be expensive, and has no guaranteed delivery, and no guaranteed delivery time. It's not suitable for real time communication.
USSD is another form of communication between a mobile device and the network that's built directly into the GSM network, but USSD messages are owned or licenced by the network operators, and aren't free for customers to use, as SMS is.
EDIT: USSD isn't a native protocol in CDMA, but various implementations are available from different operators. For example, here's a patent application describing an idea for one such system, which does not appear to require an IP connection. Googling "USSD CDMA" also gives various news items about commercial implementations, technical details unknown. I think you just have to find out what your target operator(s) offer.
I haven't worked directly with WAP, but a glance at the WAP Protocol Stack shows that it can indeed run over CDMA, or GSM without an IP connection. There is also a very useful Wikipedia article. My experience testing MMS is that it usually doesn't work without an IP connection, even though it is supposed to (according to that Wiki article, with WAP/SMS). So I would question how far European operators or mobile devices are supporting or testing WAP. Whether WAP is a practical choice could come down to pricing/availability at the end of the day, rather than technical issues.