Power side-channel analysis (SCA) has been of immense interest to most embedded designers to evaluate the physical security of the system. This work presents profiling-based cross-device power SCA attacks using deep learning techniques on 8-bit AVR microcontroller devices running AES-128. Firstly, we show the practical issues that arise in these profiling-based cross-device attacks due to significant device-to-device variations. Secondly, we show that utilizing Principal Component Analysis (PCA) based pre-processing and multi-device training, a Multi-Layer Perceptron (MLP) based 256-class classifier can achieve an average accuracy of 99.43% in recovering the first key byte from all the 30 devices in our data set, even in the presence of significant inter-device variations. Results show that the designed MLP with PCA-based pre-processing outperforms a Convolutional Neural Network (CNN) with 4-device training by ~20%in terms of the average test accuracy of cross-device attack for the aligned traces captured using the ChipWhisperer hardware.Finally, to extend the practicality of these cross-device attacks, another pre-processing step, namely, Dynamic Time Warping (DTW) has been utilized to remove any misalignment among the traces, before performing PCA. DTW along with PCA followed by the 256-class MLP classifier provides >=10.97% higher accuracy than the CNN based approach for cross-device attack even in the presence of up to 50 time-sample misalignments between the traces.