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First of all you should give your question a title pertaining to the content. And yours is very deceiving as you are not even talking about ROS here.
About your question you already have you answer: you have an IMU and you don't use it to correct the odometry, so use it.
Your AMCL is based essentially on the IMU which (unless it's a very expansive one) does a really awful job at providing movement estimations. So since you're going to filter IMU and odometry, use this for the AMCL.
If you don't have odometry, then you're in for a lot of headache. Get two encoders on the wheels.
A partial workaround would be a very precise SLAM running off the laser, but I don't know how much better could it be with jumpy positioning.
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