An IR signal is modulated. To understand the data you need to demodulate the signal. The simplest way is with an IR receiver module. However they condition the signal into a digital signal - it's impossible (on the majority of modules) to get the signal strength.
The devices you link to are IR Photodiodes. They form the optical receiver portion of the IR modules. You need to couple them with some form of demodulating system - either in hardware or, if your MCU is powerful enough, in software. However, you can get at the raw analog voltages that the photodiode generates to get a signal strength value.
So you have either an easy time of it but no signal strength, or signal strength but a very hard job of interfacing.
So why not take the best bits of both? Use an IR module to demodulate the signal and give you the data, and next to it use a photodiode and op-amp (to boost the tiny signal) to give you the raw optical intensity? Yes, it would cost you more, and the circuitry would be more complex, but it's really the only way that you can do it without using specialist modules.
But of course, it begs the question: why do you really want to get this kind of information? Of what use can it be? The "signal strength" is of little benefit since there are so many factors that influence it - incidence angle, distance, transmitter battery voltage, etc.