Can I replace the trans-axle through an access on the outside of the transmission? Or is it necessary to remove the transmission in order to change the trans-axle on a 1998 Camry?

seems to be a bit of a problem
do you have an automatic transmission or a manual
you cannot have both so if it is a clutch it is manual or if auto thee will be no clutch

The trans-axle probably has two safety switches - one for neutral and one for park. The switch that senses the shifter's park position may have failed or a connector has come loose. These switches are usually accessible from outside the trans-axle or transmission, and are not terribly expensive to replace or service. Since the vehicle starts in neutral I would just live with it for the time being.

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Remove the tire. remove the strut bolts. remove the axle nut. push the axle out of the hub(hammer out if necessary). Pull/push the hub away to get the axle completely out. Use a pry bar to get the axle out of the transmission. replace in reverse order. add fluid if necessary.

You only lost a few ounces

You warm the trans up to 180 degrees
or more & check fluid levels as you always
do & add if necessary

Why not change all the fluid while your there

That has to be done every 3 years anyway

You can do it once a year if you like

You do not add to any trans cold
Has to be at 180 or more

The diff is part of the trans axle automatic transmission assembly and is not a separate part that can be removed.

Your transmission cooler in the radiator tank is probably leaking, A radiator shop could probably replace the cooler but if the radiator is old you should replace the whole thing.

remove the axle stub retaining nut, disconnect the lower ball joint, disconnect the tie rod end, pull the spindle out and away from the axle stub tapping on the end of the stub if necessary with a hammer (just be careful) to pull the bearing hub loose from the axle stub. after separating the outside slide under vehicle (make sure the car is on jack stands and the rear wheels are blocked from rolling and very secure before crawling under any vehicle) look at where the inside axle stub goes into the transmission. you'll need a good sized pry bar to pop the axle out of the transmission. work the pry bar in between the inside axle stub and a good thick part of the transmission and pry the axle away from the trans., there is a snap ring on the inside axle stub that internally retains the axle you have to pry hard enough to compress the snap ring into the axle groove which will release the axle for removal. it's not a bad idea to replace the axle seal in the transmission while you're there but if it's not leaking and you don't damage it in the removal of the axle it's not necessary. measure and compare the new axle to the old one, it may have some differences in the shaft like missing vibration dampeners but if it's the same length and both axle stubs match the old ones in size and number of teeth you should be good. when you install the new axle line it up by hand and slide it in as far as possible manually then tap it in with a wooden or rubber mallet. if you don't have a mallet use a scrap of wood to protect the new axle stub threads and tap it in with a hammer. after you feel the snap ring collapse and the axle slide in tap on it gently to make sure it's fully seated then grab the inner axle stub and tug on it to insure the snap ring is in place. then reassemble in reverse order of removal making sure all nuts and bolts are tightened properly and all retainers are in place. good luck

USUALLY A SHIFT SOLENOID DTC IS REPAIRED BY REPLACING THE TRANS SOLENOID PACK ASSEMBLY..LOCATED ON OUTSIDE OF TRANSMISSION..YOU MUST BE CAREFUL WHEN CHANGING PACK..CLEAN ALL DIRT/DEBRIS FROM OUTSIDE OF PACK..YOU DON'T WANT ANY DIRT TO ENTER TRANSMISSION..SOLENOID IS A SMALL BOX LOCATED ON SIDE OF TRANS FACING FRONT OF VEHICLE..YOU MUST REMOVE TRANS COOLER LINE HOSES FROM FITTINGS ON TRANS..REMOVE INPUT SPEED SENSOR..UNPLUG PACK..8MM SCREW HOLDS IT..3 BOLTS HOLD PACK TO TRANS..YOU MUST CLEAN ALL GASKET RESIDUE THOROUGHLY BEFORE INSTALLING PACK..I'D RECOMMEND GETTING SOMEONE WHO HAS DONE THIS BEFORE IF YOU ARE NOT COMFORTABLE DOING THIS..I HOPE THIS HELPS

Sometimes these axles are tough to remove, sometimes you may have to tap the outside of the axle with either a brass hammer or rubber mallet (as not to damage the outer part of the axle) adthen try and pull out the axle shaft. You may also have to try pry bar behind the axle shaft (where it goes into the transmission) and slightly pry out away from the transmission to release the ring lip that holds it in place inside the transmission. Hope this helps.

remove whole axle.. take strut assembly and steering gear apart ,. then big nut at hub, pull strut/steering linkage away from axle out of center...then pop inner axle shaft out of transmission , with drip pan underneath as you will flow trans fluid from there..do both sides then separate trans and drop...good luck