The transfer times and costs of global resources between different projects and the choice of transfer modes significantly affect the multi-project scheduling. This paper investigates four versions of the resource-constrained multi-project scheduling problem with global resource transfers and local resource constraints based on four realistic transfer scenarios, in which the global resource transfer times and costs are considered with a single transfer mode or multiple transfer modes. Three classes of heuristics with huge amount of priority rules are adapted and tested for the new problems. The schedule generation schemes of each class of heuristics are improved from two aspects. On the one hand, resource availability checks are divided into global and local phases due to their different characteristics. On the other hand, resource transfer rules and transfer mode rules are introduced to deal with resource transfer and transfer mode issues, respectively. The three class of heuristics are tested on well-known datasets of the multi-project problem, which are extended with transfer data using a transfer time/cost generation procedure. The numerical experiments first evaluate the performance of a set of priority rules, then effectively apply the priority rule heuristics in the genetic algorithm, and finally compare the performance of the priority rule heuristics with CPLEX on small-scale instances. Additionally, a multi-project case study verifies the applicability and good performance of priority rules that perform well in numerical experiments. Furthermore, the best performing rules are used by two machine learning methods in literature to automatically select the most promising ones.