How to extract an out of line inner screw from the implant, after the crown portion has been removed? Tools not effective now

Despite implant durability and versatility, one must take care not to mess things up.  Fixation screws can strip or break and can lead to "very bad things".  It is best to seek care from experienced clinicians, likely a periodontist or oral surgeon.

You did not specify if the tooth was cemented with a screwed in abutment(post) or if the tooth was screwed in whole.  It sounds like your implant screw is loose & the dentist cannot engage the internal screw.  Several reasons may be the cause, not limited to;-there is debris on the screw head not allowing proper engagement of the driver-the screw head has been stripped & will not engage-the wrong tool shape is being usedthere is a broken screw removal kit that exists & should be used as a last resort

Once the crown is off, there should be the abutment and the screw that holds it in place. If the screwdriver can engage the top of the screw, it can be unscrewed IF the threads of the screw are not damaged. If the screw thread is deformed, then it may not easily rotate out. This sounds to be where your condition is. One option is to remove top of the abutment to allow exposure of the screw head all the way around. Then use a wire twister or a larger caliper with good stability to grab the top of the screw and rotate and pull at same time. If the screw is fractured at below the implant platform, this becomes a more difficult challenge. There are several techniques in how to remove the screw in this case- and if not successful, removal of the implant itself may be necessary.