Background: Very few scientific studies have simultaneously evaluated changes in well-being (WB), physical activity (PA), and strength endurance (SE) based on results from before and during the COVID-19 pandemic. Aim: The aim of the study was to assess WB, PA, and SE levels, as well as body composition parameters in university students before and during the pandemic. Methods: The study included 30 males and 30 females (mean age: 21.7 ± 2.51 and 21.6 ± 2.34 years, respectively). Well-being using the Self-Perception Questionnaire (POMS), PA from the Polish regular version of the International Physical Activity Questionnaire (IPAQ), body composition parameters using the InBody 270 analyzer, and SE based on the results of a 12 min test involving a Concept 2PM-5 rowing ergometer were assessed before and during the pandemic. Results: An assessment of university students’ WB revealed a significant increase in variables such as tension, depression, anger, confusion, and a significant decline in vigor (p < 0.05). In both sexes, PA and SE decreased significantly—from 2115.4 to 1822.8 METs-min/week and from 2184.5 to 2035 m, respectively, in males, and from 1793.5 to 1699.8 METs-min/week and from 2021.5 to 1943.8 m, respectively, in females. At the same time, body mass and BMI values increased significantly (p < 0.001) in both females and males. Conclusions: The COVID-19 pandemic caused a significant decrease in WB, PA and SE levels in young females and males, and led to a significant increase in their body mass and BMI.