If your null hypothesis is that age category will not affect religiosity score, then you could just use a chi squared test ((observed-expected)^2 / expected), where expected is an assumption of mid-score. This assumes the method you use to measure religiosity gives you a numerical score.

From what you've described, your independent variable is age category and your dependent variable is the religiosity score, which I assume to be a scale variable. If you just use the scores, a straightforward analysis would be a one-way ANOVA. However, since you've created a set of categories, Kruskal-Wallis is the non-parametric analog to ANOVA. For post hoc comparison, you can use a series of Mann-Whitney U pairwise comparison with the Bonferroni adjustment of your alpha level divided by the number of comparisons to get a lower alpha level that controls for type 1 errors. I'm wondering how categorizing your instrument scores into groups serves your research hypothesis? 

@Kevin J. Eames

Thank you very much for your answer. That what I was looking for. The title of the project (now submitted article) is "Muslim Religiosity in the Transitional Society: Traits and Measurement." I used a tested scale (Sethi and Seligman, 1993) to measure religiosity. First I run EFA, then CFA and selected 13 items, 2 (i.e. religious beliefs and religious influences) factors in accordance with the Indexes got from that.

Next, Based on equal percentile based on Scanned Cases, the Religiosity variables are categorized into three distinct categories (i.e. high=3, Medium=2, low=1). For example, if the cumulative scores of the six items loaded for the 'Religious Influence' factors remain less than 25, is considered as low, and any score above 32 indicates high influences. Hence, any score in between 26 and 31 considers as medium. Seven items loaded for the factor 'religious beliefs', and any value lies between 39 and 43 is considered as moderate level of beliefs. Any values in ‘religious beliefs’ scale lower than 25 is considered as low, and above 44 as strong beliefs. Likewise, age is categorized as childhood=1, adolescence=2, early adulthood=3... old age=6.

I ran chi-square and the test result not assuming null hypothesis. The reviewer implies that since the variables have category, the more robust test can be performed.

Primarily, the intention was to formulate a scale that is valid enough to measure religiosity in a transitional society like Bangladesh. Since, some valid relationships has been found among the religiosity variables, age and gender, I included that in the article.  Hence, hypotheses are like, religious influences changes in accordance with the age category, and religious beliefs is dynamic rather than static and in varies from age to age.

Now, do you think that I should do Kruskal-Wallis, or go back and do one-way ANOVA?

I think there are two ways to approach this. If you want to analyze age (IV) and the religiosity categories (DV), I would use Kruskal-Wallis. Another approach might be to treat your factors, religious beliefs and religious influences as distinct dependent variables and use a one-way ANOVA with each factor. The advantage to this is that your factors are scale and the ANOVA would increase the level of precision. 

Your research sounds fascinating. I hope you find it to be fruitful in your scholarship.