Do lighter-than-air aircraft communicate with ATC? If not, how do they avoid running into other aircraft?
No aircraft is required to talk to ATC, except in certain situations. Whether or not they have a radio, all pilots are required to continuously watch outside the airplane for other aircraft and to avoid them visually, much like someone driving a car avoids other cars by looking for them.
Aircraft are required to communicate with ATC only in certain situations. 14 CFR 91 contains the requirements:
- 91.126 - Within 4 miles and 2,500 ft of an airport in Class G Airspace
- 91.127 - Within 4 miles and 2,500 ft of an airport in Class E Airspace
- 91.129 - Within Class D Airspace
- 91.130 - Within Class C Airspace
- 91.131 - Within Class B Airspace
- 91.135 - Within Class A Airspace
- 91.155 - In weather conditions less than VFR
- 91.183 - While operating IFR
- 91.511 - More than 1 hour flight time or 100 miles from shore (overwater)
Many of these can be waived with prior coordination with ATC.
Outside of the above situations, no radio is required. In fact, there are still many airplanes that don't even have an electrical system, much less a radio, and they are perfectly legal to go fly around.
On the other hand, if they do have a radio (even a hand-held radio) it can greatly add to the safety of flight if they remain in contact with ATC since they can point out traffic that they might not have seen as quickly otherwise.
Now, whether or not the pilot is talking to ATC, they are required to "see and avoid" other aircraft, and certain aircraft have the right of way over other aircraft. As you can imagine, an unpowered balloon can't really get out of way of a 747, so it is the responsibility of the more maneuverable aircraft to turn to avoid hitting the less maneuverable one (see 91.113 for more details).
They are also required to remain a certain distance away from clouds (91.155). This is so that one aircraft doesn't come out of a cloud, possibly at a very high speed, and run right into another aircraft because they didn't have time to avoid them. If they are far enough away, then the pilots will have time to see and avoid each other.