Wesleyanism may also be accurately called Wesleyan Arminianism. Arminians believe in "general redemption," which is the doctine that Christ died for everyone, and not just for the elect. The type of Arminianism that Wesleyans hold to includes the belief that one can lose his salvation, which is a doctrine that Arminius himself never taught.
Besides loss of salvation, the word "Wesleyan" refers specifically to the belief in entire sanctification as a second definite work of grace subsequent to regeneration.
The Wesleyan Church was formed by the merger of two denominations in, oh, seems like '69 or something like that--the Wesleyan Methodist Church and the Pilgrim Holiness Church.
The goal of all these offshoots is to get back to the original Methodism that transformed England and evangelized America. (Good luck...)
The finest book I could recommend is Skevington Wood's The Burning Heart, a glorious biography of John Wesley and an exposition of his thought.