How to Improve filtered_odom results

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I think there are a couple things going on.

1. I think you may have an unrealistic expectation of what a state estimator like an EKF is going to do. You are providing one source of pose data from your wheel encoders. If the issue with your raw wheel odometry is that it is under- or over-estimating linear motion, the EKF won't fix that for you.
2. You are fusing absolute yaw from the wheel encoders, but the wheel encoder data is reporting very small errors; your yaw variance is 1.597e-9, which means you have a standard deviation of 3.99e-05. That seems unlikely. In any case, your IMU yaw velocity will get fused with that, but it's getting integrated first, so it won't have a strong effect.

In other words, you are fusing two sources of information into the EKF, but you are telling the EKF to really, really trust one source. And you won't be able to remove issues with uncalibrated wheel encoder data. If the wheel encoders are consistently under-reporting their position change, then that will get reflected in the EKF output.

I would only use velocity for your wheel encoder data if the wheel encoders themselves directly produce it. Just doing differentiation on the wheel encoder positions and sending that to the EKF to be integrated again won't solve anything. It's also what differential mode does anyway, so there would be no need to implement that in the wheel encoder generation node.

EDIT in response to comments:

find out whether my raw wheel odometry is under or overestimating the linear motion

I'd drive it in a long, straight line over a known distance (you'd have to measure this physically), and then compare the reported linear distance to the actual. I'd also recommend that you implement wheel odometry calibration. There are numerous sources for this online.

I am wondering how can I change these variance values to the required values

Is the odometry sensor closed source? If it's open source, you can look what the code is doing, or even fork it, fix it, and build it yourself. If the odometry sensor puts out joint state info, you might also consider using something like the differential drive controller in ros_control.

In general, I prefer odometry sources that let me work directly with velocity, rather than with absolute pose data. But pose data works too, provided that the covariance is correct.