We know that OFDM eliminates the inter-block intereference. But there are still multipath interference in a single OFDM block(symbol). How does LTE handle this intra-block interference induced by multipath components so as to successfully demod. the signal ?
By using cyclic prefix and its associated demodulation techniques, LTE OFDM (nearly) eliminates the inter-symbol inteference (ISI). The intra-block inteference, if I understand well your question, refers to intra-carrier inteference (ICI) when the orthogonality between sub-carriers is not maintained due to Doppler, delay spread too large, synchronisation error, ...
Ignoring equipment default that can be mitigated by using sub-carrier pilots, all remaining errors are expected to be fixed by powerful channel coding. Of course the less errors before entering to channel decoder, the better the final result is.
Please note that LTE sub-carrier spacing 15KHz and 7.5Khz are well-chosen so that it is smaller than the coherence bandwidth of typical power delay profiles. Then each sub-carrier is in flat-fading, no ICI if orthogonality is maintained.
Another thing to note that even with the latest modern channel codes, a very long codeword are required to achieve comfortable performance. Inteleaver helps to reduce the length.
So, to be short, after eliminating ISI, remaining errors are corrected mainly by channel code, with helps of pilots, inteleaver and parameter dimensionning.