Virtually anything along those lines is possible: The only thing it takes is enough money, or skill, or both to cover all the work. People have put a small block Chevy V-8 into a 1960's Austin Healey Sprite (which is a tiny roadster that probably weighs about 1,000 pounds). I know someone who put a Chevy into a Datsun 510, and someone else who put one into an old Mazda RX-2. These cars are dangerous to drive; because they have so much power for their size and weight that they can do wheelstands, or go out of control; if the driver is not up to handling the performance potential.
The Dodge Avenger is a front wheel drive vehicle. If you put a Hemi into it; it would be necessary to convert it to rear wheel drive; as neither the stock front axles nor the front suspension could handle the power. And there are no Hemi FWD transmissions; they all are rear wheel drive. But stock car racers often convert FWD cars to RWD; when they replace the V-6 motors with powerful V-8s, for the same reasons. Please understand that paying competent people to make modifications of that level would cost at least $20,000, and very likely twice that much; and that is in addition to the cost of the engine and the transmission. If you're driving a 16 year old car, and planning on continuing to run it until it quits; this doesn't sound like you are or will be in a financial position to pay for this kind of stuff. A new Hemi high performance motor (you wouldn't want to put an old, tired Hemi into a project of this level) will cost you between $12,000 and $20,000; just for the bare engine. The suspension and body would also have to be strengthened to withstand the torque it will be subjected to. The springs would have to be replaced with stronger ones to just handle the increased engine weight. The rear axle and rear suspension would have to be totally changed. The body might have to be widened to accept the Hemi's bulk. And you would end up with an illegal vehicle which could not be driven on public roads. By the time it was all done; you probably could have bought 2 brand new Hemi powered Dodge Challengers for less than this project would cost. And the Challenger does have enough power for its look; and it is smog legal, smooth riding, and put together right; in a balance that probably could never be matched by patching up an old car.