As far as my knowledge goes:

The eagle on the bottom right of the secod picture is the insignia of the 101st airborne division (same division of which Easy company was part of as seen in Band of Brothers, although they were part of the 506th Infantry Regiment)

The little parachute pin on the bottem right of the first pics are his "jump wings". This means he succesfully earned them by completig the course of parachuting during training. Having recieved this badge means he has completed this traing succesfully and was a fully trained paratrooper.

This was wat I am certain about, now for the two big patches in the first picture. Well you probably heard of Bastogne I guess? Otherwise you can look up "Battle of the Bulge". My guess is he recieved this patch after taking part in the battle. Same goes for the Eindhoven patch, this was part of Operation Market Garden, which was evetually a failed operation by the allies. Having been in Eindhoven makes me guess he was part of the 506th Infantry Regiment but this is speculation of my part, others will have to verify this.

I have hoped this helped you a bit further already, I am sorry I don't know more! (I wish I knew more though!)

To add to what was already posted. The circular pin with the US on it would’ve been on his dress uniform for enlisted personnel. To the right of that is his unit crest. Also would’ve been in his dress uniform. The red and white ribbon is the Army Good Conduct Medal, awarded for three years of honorable service. Below that is the combat infantry badge, given to infantryman who participated in active ground combat. And to the right of the Army Good Conduct Medal it looks like a unit award with a oak leaf cluster. Sorry for the bad formatting I’m on mobile. I hope I could help some.

To fill in the information gaps from the previous answers:

The unit crest to the right of the U.S. insignia is associated with what is currently the 276th Engineer Battalion, but at the time your great uncle received it, it was more than likely associated with the 2nd Battalion, 176th Infantry. This is drawing from an assumption of the timeline given the Combat Infantry Badge, the campaign patches, and the lineage information. Without records it is hard to draw solid conclusions, but it is likely he was in this unit in a pre-deployment capacity prior to moving to the 101st.

The blue ribbon on the top right is the Presidential Unit Citation, with a single bronze oak leaf. The Presidential Unit Citation is the highest unit award that can be received and is the collective equivalent of the Distinguished Service Cross. Having this award, with the oak leaf cluster, indicates that the person wearing it was in the unit when the unit received two of these awards.

As for the patches on the bottom, the left one is associated with glider units. This was a very dangerous position to be in, the personnel assigned to these units were towed in a glider behind another aircraft and detached when they neared their target. The glider would then glide, hopefully to a soft landing, in the target area. The middle patch is associated with the 502nd Infantry Regiment (possibly 3rd battalion from memory, but I can't find a source confirming this) under the 101st Airborne Division (the eagle patch on the right).

Hello there! As your question is related to looking for identification/information regarding military personnel, our Guide on Military Identification may be of use to you. It provides a number of different resources, including how to request service records from a number of national agencies around the world, as well as graphical aids to assist in deciphering rank, unit, and other forms of badges or insignia. While the users here may still be able to lend you more assistance, hopefully this will provide a good place to start!