Is it possible to create a DbContext Interface or abstract class and use it to inject different DbContext Objects?

No, there isn't. But you can always build one like this:

interface IDbContext : IDisposable
{
    DbSet<TEntity> Set<TEntity>() where TEntity : class;

    Task<int> SaveChangesAsync();
}

public class MyDbContext : DbContext, IDbContext
{
    public MyDbContext()
        : base("myConnectionString")
    { }

    //implementation
}

And inject IDbContext when needed.