How can the Armored Titan and Annie in the Titan form harden their bodies, while Eren and the other Titan Shifters can't?
The fact that Annie can harden her Titan form and Eren couldn't is because there are different types of Titan power in existence.
The complete explanation is as below.
Massive Spoiler Alert
In the manga it is later revealed that all Titan powers came from Ymir Fritz, an ancient Fritz family monarch. According to Eldian mythology, over 1,820 years ago, Ymir came across what is only described as the "source of all organic material". With this discovery, Ymir gained the power of the Titans, becoming the 'Progenitor of all Titans'.
After 13 years Ymir met her death, and her "soul" was split between nine successors, giving these nine Titan powers. Throughout history, these powers are inherited by the 'Eldians' or the 'Subjects of Ymir'.
The Titan power that Eren possesses is called the 'Attack Titan'(進撃の巨人 Shingeki no Kyojin). The names of powers of other Titan Shifters is not yet revealed but they are also among the nine.
This the reason that the Titan Shifters possess different powers.