Generally, saying blessings, studying Torah aloud, and thinking about Torah matters are all prohibited when in the presence of a foul odor. As the Shulkhan Aruch states (OC 85:2):
א אפי' להרהר בד"ת, אסור בבית הכסא ובבית המרחץ ובמקום הטנופת, והוא
המקום שיש בו צואה ומי רגלים. הגה: ואפי' הלכות המרחץ אסור ללמוד במרחץ
(ר"ן פ' כירה וב"י בשם א"ח). דברים של חול, מותר לאמרם שם בלשון הקדש.
וכן הכנויים, כגון רחום, נאמן וכיוצא בהם, מותר לאמרם שם; אבל השמות
שאינם נמחקין, אסור להזכירם שם. ואם נזדמן לו שם להפריש מדבר האסור,
מפריש, ואפילו בלשון הקודש ובענייני קודש. הגה: ובמקום שמותר להרהר בד"ת,
מותר לפסוק דין ובלבד שלא יאמר טעמו של דבר (ר"ן פ"ק דשבת ובפרק כל
הצלמים.
It is even forbidden to think of Torah matters when in the bathroom or in a bathhouse or in some place of filth, which is a place where there is feces and urine.
Rama: And it is even forbidden to learn Torah in a bath (cf. Ran).
It is permissible to refer to Hashem matters in the holy language
[Hebrew]. And those names, like Rachum, Neeman, and their derivates are allowed
to be said. But for names that can't be erased, it is forbidden to
bring them up. If it happens that he needs to separate himself from
something forbidden, he should separate from it even if that includes
the holy language and holy matters. [Mishnah Berurah: if a sinful
thought entered his heart, you're allowed to think of Torah matters
because that is like setting aside a prohibition; the Torah saves you
from the evil thought]
Rama: And in a place where it is permissible to think of Torah matters it is permissible to render judgments as long as no reason is provided
(cf. Ran). [Mishnah Berurah: For example, in the adjoining room to the bath or if he himself is not completely clean because, for example, his hands touched a covered part of his body. But if his hands or other places on his body are mamash disgusting, even thinking is prohibited.]
So if you are not allowed to say God's name, you can't say a blessing. And not only can you not study Torah aloud, you're not even allowed to think about Torah matters.
Nevertheless, there are many provisions to these halakhot. For example, the sugya in Brachot 25 (which is where the halakhot of odors are brought down) mentions certain animals as being under the same category as human feces, while others may not necessarily be included. Additionally, some odors which are not natural decomposing wastes might not be included in these prohibitions. So, you have to define what you mean by a "bad smell." If you mean feces and urine, then all five activities are prohibited.
