This is completely implementation-dependent, but there are a few factors that influence object size in Java.
First, the number and types of the fields in the Java object definitely influence space usage, since you need to have at least as much storage space as is necessary to hold all of the object's fields. However, due to padding, alignment, and pointer compression optimizations, there is no direct formula you can use to compute precisely how much space is being used this way.
As for methods, typically speaking the number of methods in an object has no impact on its size. Methods are often implemented using a feature called virtual function tables (or "vtables") that make it possible to invoke methods through a base class reference in constant time. These tables are usually stored by having a single instance of the vtable shared across multiple objects, then having each object store a single pointer to the vtable.
Interface methods complicate this picture a bit, because there are several different implementations possible. One implementation adds a new vtable pointer for each interface, so the number of interfaces implemented may affect object size, while others do not. Again, it's implementation dependent how things are actually put together in memory, so you can't know for certain whether or not this will have a memory cost.
To the best of my knowledge there are no implementations of the JVM in existence today in which the length of a method influences the size of an object. Typically, only one copy of each method is stored in memory, and the code is then shared across all instances of a particular object. Having longer methods might require more total memory, but should not impact the per-object memory for instances of a class. That said, the JVM spec makes no promises that this must be the case, but I can't think of a reasonable implementation that would expend extra space per object for method code.
In addition to fields and methods, many other factors could contribute to the size of an object. Here's a few:
Depending on what type of garbage collector (or collectors) that the JVM is using, each object might have extra storage space to hold information about whether the object is live, dead, reachable, etc. This can increase storage space, but it's out of your control. In some cases, the JVM might optimize object sizes by trying to store the object on the stack instead of the heap. In this case, the overhead may not even be present for some types of objects.
If you use synchronization, the object might have extra space allocated for it so that it can be synchronized on. Some implementations of the JVM don't create a monitor for an object until it's necessary, so you may end up having smaller objects if you don't use synchronization, but you cannot guarantee that this will be the case.
Additionally, to support operators like instanceof and typecasting, each object may have some space reserved to hold type information. Typically, this is bundled with the object's vtable, but there's no guarantee that this will be true.
If you use assertions, some JVM implementations will create a field in your class that contains whether or not assertions are enabled. This is then used to disable or enable assertions at runtime. Again, this is implementation-specific, but it's good to keep in mind.
If your class is a nonstatic inner class, it may need to hold a reference to the class that contains it so that it can access its fields. However, the JVM might optimize this away if you never end up using this.
If you use an anonymous inner class, the class may need to have extra space reserved to hold the final variables that are visible in its enclosing scope so that they can be referenced inside the class. It's implementation-specific whether this information is copied over into the class fields or just stored locally on the stack, but it can increase object size.
Some implementations of Object.hashCode() or System.identityHashCode(Object) may require extra information to be stored in each object that contains the value of that hash code if it can't compute it any other way (for example, if the object can be relocated in memory). This might increase the size of each object.
