This paper presents a deep learning system applied for detecting anomalies from respiratory sound recordings. Initially, our system begins with audio feature extraction using Gammatone and Continuous Wavelet transformation. This step aims to transform the respiratory sound input into a two-dimensional spectrogram where both spectral and temporal features are presented. Then, our proposed system integrates Inception-residual-based backbone models combined with multi-head attention and multi-objective loss to classify respiratory anomalies. Instead of applying a simple concatenation approach by combining results from various spectrograms, we propose a linear combination, which has the ability to regulate equally the contribution of each individual spectrogram throughout the training process. To evaluate the performance, we conducted experiments over the benchmark dataset of SPRSound (The Open-Source SJTU Paediatric Respiratory Sound) proposed by the IEEE BioCAS 2022 challenge. As regards the Score computed by an average between the average score and harmonic score, our proposed system gained significant improvements of 9.7%, 15.8%, 17.8%, and 16.1% in Task 1–1, Task 1–2, Task 2–1, and Task 2–2, respectively, compared to the challenge baseline system. Notably, we achieved the Top-1 performance in Task 2–1 and Task 2–2 with the highest Score of 74.5% and 53.9%, respectively.