We apply three different methods based on the analysis of the multi-component seismic data to detect seismovolcanic tremors and other seismovolcanic signals, to propose an approach to classify them and to locate their sources. We use continuous seismograms recorded during one year by 21 stations at the Piton de la Fournaise volcano (La Réunion, France). The first method allows to detect seismovolcanic signals based on stability in time of the inter-components cross-correlations function. Two other methods based on the simultaneous analysis of the whole network can be used to detect seismovolcanic signals and to locate their sources. In a second approach, the seismic wavefield is analyzed by calculating the width of the network covariance matrix eigenvalue distribution. The third method consists in performing the 3D back-projection of the inter-stations crosscorrelations in order to calculate the network response function. Simultaneous analysis of the parameters measured by the three different methods can be used to classify different types of seismovolcanic tremors. Our results demonstrate that all three methods efficiently detect seismovolcanic tremors accompanying the 2010 eruptions and the preceding pre-eruptive seismic swarms. Furthermore, methods 2 and 3 based on simultaneous analysis of the whole network detect a large number of volcanic earthquakes. Our location results show that each seismovolcanic tremor is located in a distinct region of the volcano, close to the eruptive site at a shallow depth and the preceding seismic crisis is located deeper at about the sea level under the summit crater.