With the global population aging rapidly, Alzheimer's disease (AD) is particularly prominent in older adults, which has an insidious onset and leads to a gradual, irreversible deterioration in cognitive domains (memory, communication, etc.). Speech-based AD detection opens up the possibility of widespread screening and timely disease intervention. Recent advances in pre-trained models motivate AD detection modeling to shift from low-level features to high-level representations. This paper presents several efficient methods to extract better AD-related cues from high-level acoustic and linguistic features. Based on these features, the paper also proposes a novel task-oriented approach by modeling the relationship between the participants' description and the cognitive task. Experiments are carried out on the ADReSS dataset in a binary classification setup, and models are evaluated on the unseen test set. Results and comparison with recent literature demonstrate the efficiency and superior performance of proposed acoustic, linguistic and task-oriented methods. The findings also show the importance of semantic and syntactic information, and feasibility of automation and generalization with the promising audio-only and task-oriented methods for the AD detection task.