In this era of technological advancement, the flow of an enormous amount of information has become such an inevitable phenomenon that makes a path for the takeover of the internet of things (IoT) based smart grid from the currently available grid system. In a smart grid, demand-side management plays a crucial role in reducing the generation capacity by shifting the user energy consumption from peak period to off-peak period, which requires detailed knowledge of the user consumption at the individual appliance level. Non-intrusive load monitoring (NILM) provides an exceptionally low-cost solution for determining individual appliance levels using a single-point measurement. This paper proposed an IoT-based real-time non-intrusive load classification (RT-NILC) system considering the variability of supply voltage using low-frequency data. Due to the unavailability of smart meters at the household level in Bangladesh, a data-acquisition system (DAS) is developed. The DAS is capable of measuring and storing rms voltage, rms current, active power, and power factor data at a sampling rate of 1 Hz. These data are processed to train different multilabel classification models. The best-performed classification model has been selected and utilized for the implementation of RT-NILC over IoT. The Firebase real-time online database is considered for data storage to flow the data in two-way between end-user and service provider (energy distributor). The GPRS module is used for wireless data transmission as a Wi-Fi network may not be available everywhere. Windows and web applications are developed for data visualization. The proposed system has been validated in real-time, using rms voltage, rms current, and active power measurements at a real house. Even under supply voltage variability, the performance evaluation of the RT-NILC system has shown an average classification accuracy of more than 94%. Good classification accuracy and the overall operation of the IoT-based information exchange systems ensure the proposed system's applicability for efficient energy management.