It depends on what is meant by "ex-" and the rules are different for each of the two classes. Basically the RAW defines "ex-" as no longer being able to advance in that class. That is the single commonality in all the text/conditions.
A paladin loses all benefits if he ceases to be lawful good. . . . .
But he retains those abilities if he changes classes, he just can no longer advance as a paladin.
A monk on the other hand retains all abilities if he becomes non-lawful but can no nonger advance as a monk. The same applies if he changes classes.
They cannot however continue to advance in the paladin or monk class unless the prestige class so states (the ones that allow it state so). There are feats (specifically in Eberron) that allow paladins and monks to freely multiclass with another class.
SRD
A paladin loses all benefits if he ceases to be lawful good. . . . .
But he retains those abilities if he changes classes, he just can no longer advance as a paladin.
A monk on the other hand retains all abilities if he becomes non-lawful but can no nonger advance as a monk. The same applies if he changes classes.
They cannot however continue to advance in the paladin or monk class unless the prestige class so states (the ones that allow it state so). There are feats (specifically in Eberron) that allow paladins and monks to freely multiclass with another class.
SRD
Ex-Paladins
A paladin who ceases to be lawful good, who willfully commits an evil act, or who grossly violates the code of conduct loses all paladin spells and abilities (including the service of the paladin’s mount, but not weapon, armor, and shield proficiencies). She may not progress any farther in levels as a paladin. She regains her abilities and advancement potential if she atones for her violations (see the atonement spell description), as appropriate.
Like a member of any other class, a paladin may be a multiclass character, but multiclass paladins face a special restriction. A paladin who gains a level in any class other than paladin may never again raise her paladin level, though she retains all her paladin abilities.
Ex-Monks
A monk who becomes nonlawful cannot gain new levels as a monk but retains all monk abilities.
Like a member of any other class, a monk may be a multiclass character, but multiclass monks face a special restriction. A monk who gains a new class or (if already multiclass) raises another class by a level may never again raise her monk level, though she retains all her monk abilities.